\relax 
\citation{Cox-Katz}
\@writefile{toc}{\contentsline {section}{\tocsection {}{}{Introduction}}{1}}
\@writefile{toc}{\contentsline {subsection}{\tocsubsection {}{0.1}{Gromov--Witten invariants in the smooth case}}{1}}
\citation{Chen-Ruan}
\citation{AGV}
\citation{Abramovich-Vistoli}
\citation{Li-Ruan}
\citation{Ionel-Parker1}
\citation{Ionel-Parker2}
\citation{Li1}
\citation{Li2}
\citation{Ran}
\citation{Harris-Mumford}
\citation{Mochizuki}
\citation{Hirschowitz}
\citation{Alexander-Hirschowitz}
\citation{Caporaso-Harris}
\citation{Bernstein}
\citation{Vakil}
\citation{Gathmann}
\@writefile{toc}{\contentsline {subsection}{\tocsubsection {}{0.2}{Invariants of pairs and degenerate varieties}}{2}}
\@writefile{toc}{\contentsline {subsection}{\tocsubsection {}{0.3}{The twisting method}}{3}}
\@writefile{toc}{\contentsline {subsection}{\tocsubsection {}{0.4}{The degeneration formula}}{4}}
\newlabel{maintheorem}{{0.4.1}{4}}
\@writefile{toc}{\contentsline {subsubsection}{\tocsubsubsection {}{0.4.2}{User's guide - left hand side}}{4}}
\@writefile{toc}{\contentsline {paragraph}{\tocparagraph {}{}{1}}{4}}
\@writefile{toc}{\contentsline {paragraph}{\tocparagraph {}{}{2}}{4}}
\@writefile{toc}{\contentsline {paragraph}{\tocparagraph {}{}{3}}{4}}
\@writefile{toc}{\contentsline {paragraph}{\tocparagraph {}{}{4}}{4}}
\@writefile{toc}{\contentsline {paragraph}{\tocparagraph {}{}{5}}{4}}
\@writefile{toc}{\contentsline {paragraph}{\tocparagraph {}{}{6}}{5}}
\@writefile{toc}{\contentsline {paragraph}{\tocparagraph {}{}{7}}{5}}
\@writefile{toc}{\contentsline {paragraph}{\tocparagraph {}{}{8}}{5}}
\@writefile{toc}{\contentsline {paragraph}{\tocparagraph {}{}{9}}{5}}
\@writefile{toc}{\contentsline {subsubsection}{\tocsubsubsection {}{0.4.3}{Right hand side}}{5}}
\@writefile{toc}{\contentsline {paragraph}{\tocparagraph {}{}{1}}{5}}
\@writefile{toc}{\contentsline {paragraph}{\tocparagraph {}{}{2}}{5}}
\@writefile{toc}{\contentsline {paragraph}{\tocparagraph {}{}{3}}{5}}
\@writefile{toc}{\contentsline {paragraph}{\tocparagraph {}{}{4}}{5}}
\@writefile{toc}{\contentsline {paragraph}{\tocparagraph {}{}{5}}{5}}
\@writefile{toc}{\contentsline {paragraph}{\tocparagraph {}{}{6}}{5}}
\@writefile{toc}{\contentsline {paragraph}{\tocparagraph {}{}{7}}{5}}
\@writefile{toc}{\contentsline {paragraph}{\tocparagraph {}{}{8}}{5}}
\@writefile{toc}{\contentsline {paragraph}{\tocparagraph {}{}{9}}{5}}
\@writefile{toc}{\contentsline {paragraph}{\tocparagraph {}{}{10}}{5}}
\citation{Olsson-log-cotangent}
\citation{Kim}
\citation{M-P}
\citation{degrev2}
\@writefile{toc}{\contentsline {subsection}{\tocsubsection {}{0.5}{The logarithmic approach}}{6}}
\@writefile{toc}{\contentsline {subsection}{\tocsubsection {}{0.6}{Further directions}}{6}}
\citation{degrev2}
\citation{degrev2}
\citation{Costello}
\citation{Manolache}
\@writefile{toc}{\contentsline {subsection}{\tocsubsection {}{0.7}{Outline of the paper}}{7}}
\@writefile{toc}{\contentsline {subsection}{\tocsubsection {}{0.8}{Conventions}}{8}}
\@writefile{toc}{\contentsline {subsection}{\tocsubsection {}{0.9}{Notation}}{8}}
\citation{Abramovich-Vistoli}
\citation{ACV}
\@writefile{toc}{\contentsline {subsection}{\tocsubsection {}{}{Acknowledgements}}{9}}
\@writefile{toc}{\contentsline {section}{\tocsection {}{1}{Roots and twists}}{9}}
\newlabel{S:Roots}{{1}{9}}
\newlabel{SS:tw-curves}{{1.1}{9}}
\@writefile{toc}{\contentsline {subsection}{\tocsubsection {}{1.1}{Twisted curves}}{9}}
\newlabel{SSS:aut-tw-curve}{{1.1.1}{9}}
\@writefile{toc}{\contentsline {subsubsection}{\tocsubsubsection {}{1.1.1}{Automorphism groups of twisted curves}}{9}}
\citation{AJ}
\citation{ACV}
\citation{Cime}
\citation{Olsson-twisted}
\newlabel{SSS:def-tw-curve}{{1.1.2}{10}}
\@writefile{toc}{\contentsline {subsubsection}{\tocsubsubsection {}{1.1.2}{Deformations of twisted curves}}{10}}
\newlabel{SSS:def-tw-untw}{{1.1.3}{10}}
\@writefile{toc}{\contentsline {subsubsection}{\tocsubsubsection {}{1.1.3}{Comparing deformations and automorphisms of ${\mathcal  C}$ and $C$}}{10}}
\citation{AGV}
\citation{Olsson-twisted}
\citation{Cime}
\citation{Aramovich-Vistoli}
\citation{AGV}
\citation{Cadman1}
\citation{Matsuki-Olsson}
\newlabel{SSS:mod-tw-curve}{{1.1.4}{11}}
\@writefile{toc}{\contentsline {subsubsection}{\tocsubsubsection {}{1.1.4}{Moduli of twisted curves}}{11}}
\newlabel{SS:root}{{1.2}{11}}
\@writefile{toc}{\contentsline {subsection}{\tocsubsection {}{1.2}{Root stacks}}{11}}
\@writefile{toc}{\contentsline {subsubsection}{\tocsubsubsection {}{1.2.1}{Power morphisms}}{11}}
\@writefile{toc}{\contentsline {subsubsection}{\tocsubsubsection {}{1.2.2}{Root stack of a line bunle}}{11}}
\@writefile{toc}{\contentsline {subsubsection}{\tocsubsubsection {}{1.2.3}{Root of a divisor}}{12}}
\@writefile{toc}{\contentsline {subsubsection}{\tocsubsubsection {}{1.2.4}{Roots with several divisors}}{12}}
\newlabel{SSS:compare-roots}{{1.2.5}{12}}
\@writefile{toc}{\contentsline {subsubsection}{\tocsubsubsection {}{1.2.5}{Comparison of roots}}{12}}
\citation{AGV}
\@writefile{toc}{\contentsline {subsubsection}{\tocsubsubsection {}{1.2.6}{Twisted curves as root stacks: the markings}}{13}}
\@writefile{toc}{\contentsline {subsubsection}{\tocsubsubsection {}{1.2.7}{Triviality of relative automorphisms}}{13}}
\@writefile{toc}{\contentsline {subsubsection}{\tocsubsubsection {}{1.2.8}{Inertia of root stacks when $X$ is a scheme}}{13}}
\@writefile{toc}{\contentsline {subsubsection}{\tocsubsubsection {}{1.2.9}{Inertia of root stacks when $X$ is an orbifold}}{14}}
\newlabel{L:rig-in-gerbe-c}{{1.2.10}{14}}
\citation{Cadman1}
\citation{Cadman1}
\citation{Cadman1}
\@writefile{toc}{\contentsline {subsection}{\tocsubsection {}{1.3}{Maps and lifts}}{15}}
\newlabel{L:lift-pd-pair}{{1.3.1}{15}}
\newlabel{L:eval-lift-c}{{1.3.3}{15}}
\citation{ACFW}
\citation{Borne-Vistoli}
\citation{AGV}
\newlabel{balanced_node}{{1.4}{16}}
\@writefile{toc}{\contentsline {subsection}{\tocsubsection {}{1.4}{Twisting along a nodal divisor}}{16}}
\newlabel{D:twist-node}{{1.4.1}{16}}
\newlabel{2_pushout}{{1.4.3}{16}}
\@writefile{toc}{\contentsline {subsubsection}{\tocsubsubsection {}{1.4.3}{Gluing as pushout}}{16}}
\citation{Cime}
\newlabel{SSS:bal-node-aut}{{1.4.5}{17}}
\@writefile{toc}{\contentsline {subsubsection}{\tocsubsubsection {}{1.4.5}{Automorphisms}}{17}}
\citation{Olsson-twisted}
\newlabel{SS:bal-node-def}{{1.4.8}{18}}
\@writefile{toc}{\contentsline {subsubsection}{\tocsubsubsection {}{1.4.8}{}}{18}}
\newlabel{SSS:tw-c-tw-n}{{1.4.9}{18}}
\@writefile{toc}{\contentsline {subsubsection}{\tocsubsubsection {}{1.4.9}{Twisted curves and twisted nodes}}{18}}
\@writefile{toc}{\contentsline {subsubsection}{\tocsubsubsection {}{1.4.10}{Maps and lifts}}{18}}
\newlabel{L:lift-pd-node}{{1.4.11}{18}}
\citation{Li1}
\citation{Graber-Vakil}
\citation{ACFW}
\@writefile{toc}{\contentsline {section}{\tocsection {}{2}{Expanded pairs and degenerations}}{19}}
\newlabel{S:Expansions}{{2}{19}}
\@writefile{toc}{\contentsline {subsection}{\tocsubsection {}{2.1}{Expanded pairs}}{19}}
\@writefile{toc}{\contentsline {subsubsection}{\tocsubsubsection {}{2.1.4}{Stacks of expanded pairs}}{20}}
\newlabel{D:exp-pairs}{{2.1.5}{20}}
\newlabel{item-3}{{3}{20}}
\citation{ACFW}
\citation{Graber-Vakil}
\citation{ACFW}
\newlabel{Prop:cT}{{2.1.6}{21}}
\newlabel{Rmk:cT-gen-def}{{2.1.7}{21}}
\@writefile{toc}{\contentsline {subsubsection}{\tocsubsubsection {}{2.1.7}{Defining the stack of expansions in general}}{21}}
\citation{ACFW}
\@writefile{toc}{\contentsline {subsubsection}{\tocsubsubsection {}{2.1.8}{Charts for the stacks}}{22}}
\newlabel{expdeg}{{2.2}{23}}
\@writefile{toc}{\contentsline {subsection}{\tocsubsection {}{2.2}{Twisted expanded degenerations}}{23}}
\newlabel{degeneration_conv}{{2.2.1}{23}}
\newlabel{D:exp-degs}{{2.2.3}{23}}
\citation{ACFW}
\newlabel{P:fTtw-fTu}{{2.2.4}{24}}
\newlabel{SSS:fT-gen-def}{{2.2.5}{24}}
\@writefile{toc}{\contentsline {subsubsection}{\tocsubsubsection {}{2.2.5}{Definition in general and charts}}{24}}
\citation{ACFW}
\newlabel{I:fT-gen-def-fam}{{6}{25}}
\@writefile{toc}{\contentsline {subsection}{\tocsubsection {}{2.3}{The singular case in the absence of smoothing}}{25}}
\newlabel{SS:spl-exp}{{2.4}{26}}
\@writefile{toc}{\contentsline {subsection}{\tocsubsection {}{2.4}{Split expansions}}{26}}
\newlabel{L:tw-1/r}{{2.4.1}{26}}
\citation{AGV}
\citation{Costello}
\citation{ACFW}
\newlabel{L:gl-1/r}{{2.4.2}{27}}
\newlabel{weighted-expansions}{{2.5}{27}}
\@writefile{toc}{\contentsline {subsection}{\tocsubsection {}{2.5}{Weighted and ${\mathfrak  {r}}$-twisted expansions}}{27}}
\@writefile{toc}{\contentsline {subsubsection}{\tocsubsubsection {}{2.5.1}{${\boldsymbol  {\Delta }}$-weighted expansions}}{27}}
\citation{Costello}
\@writefile{toc}{\contentsline {subsubsection}{\tocsubsubsection {}{2.5.2}{${\mathfrak  {r}}$-twisted expansions}}{28}}
\newlabel{compare-twisted}{{2.5.3}{28}}
\newlabel{P:untwisting-proper}{{2.5.4}{28}}
\citation{Kim-Sato}
\citation{ACFW}
\citation{Kim-Sato}
\@writefile{toc}{\contentsline {subsection}{\tocsubsection {}{2.6}{Stable expanded configurations}}{29}}
\citation{Kim-Sato}
\citation{ACFW}
\citation{Li1}
\newlabel{prop_deg_n}{{2.6.4}{30}}
\@writefile{toc}{\contentsline {section}{\tocsection {}{3}{Stacks of twisted stable maps and their properness}}{30}}
\newlabel{S:Stablemaps}{{3}{30}}
\@writefile{toc}{\contentsline {subsection}{\tocsubsection {}{3.1}{Conventions on stacks of maps}}{30}}
\newlabel{C:deg-data}{{3.1.1}{30}}
\newlabel{C:pair-data}{{3.1.2}{30}}
\citation{Li1}
\citation{Abramovich-Vistoli}
\newlabel{pointsincK}{{3.1.6}{32}}
\@writefile{toc}{\contentsline {subsection}{\tocsubsection {}{3.2}{Transversal maps and predeformable maps}}{32}}
\citation{Li1}
\citation{Li1}
\citation{Li1}
\newlabel{D:predeformable}{{3.2.4}{33}}
\@writefile{toc}{\contentsline {subsubsection}{\tocsubsubsection {}{3.2.5}{Contact orders and Li's predeformability}}{33}}
\newlabel{pd-is-pd}{{3.2.6}{33}}
\newlabel{L:trans-prop}{{3.2.7}{34}}
\citation{Li1}
\citation{Li1}
\citation{Li1}
\citation{Li1}
\citation{Li2}
\newlabel{predefisclosed}{{3.2.8}{35}}
\newlabel{Sec:proper}{{3.3}{36}}
\@writefile{toc}{\contentsline {subsection}{\tocsubsection {}{3.3}{Properness of the stack of predeformable maps}}{36}}
\newlabel{noclospd}{{3.3.1}{36}}
\newlabel{notval}{{3.3.2}{36}}
\citation{Li1}
\newlabel{propfp}{{3.3.3}{37}}
\newlabel{propermappd}{{3.3.4}{37}}
\newlabel{valcomdiapd}{{3.3.5}{37}}
\newlabel{eqlift}{{3.3.6}{38}}
\newlabel{uniqstbl}{{3.3.8}{38}}
\citation{Abramovich-Vistoli}
\newlabel{ndifstbl}{{3.3.9}{39}}
\newlabel{stblifnd}{{3.3.10}{39}}
\newlabel{C:pd-proper}{{3.3.11}{39}}
\citation{ACW}
\@writefile{toc}{\contentsline {subsection}{\tocsubsection {}{3.4}{${\mathfrak  {r}}$--twisted stable maps and their properness}}{40}}
\newlabel{D:twistingchoice}{{3.4.1}{40}}
\newlabel{comptc}{{3.4.2}{40}}
\newlabel{D:rtsm}{{3.4.5}{40}}
\newlabel{twistprop}{{3.4.7}{41}}
\citation{degrev2}
\@writefile{toc}{\contentsline {section}{\tocsection {}{4}{Relative and degenerate Gromov-Witten invariants}}{42}}
\newlabel{S:Invariants}{{4}{42}}
\@writefile{toc}{\contentsline {subsection}{\tocsubsection {}{4.1}{Curve classes and orbifold cohomology on nodal DM stacks}}{42}}
\newlabel{DGWI}{{4.2}{42}}
\@writefile{toc}{\contentsline {subsection}{\tocsubsection {}{4.2}{Gromov--Witten invariants for nodal DM stacks}}{42}}
\newlabel{D:ev-deg}{{4.2.1}{42}}
\citation{AGV}
\citation{AGV}
\newlabel{RGWI}{{4.3}{43}}
\@writefile{toc}{\contentsline {subsection}{\tocsubsection {}{4.3}{Relative Gromov--Witten invariants}}{43}}
\newlabel{D:ev-pair}{{4.3.1}{44}}
\newlabel{goodass}{{1}{44}}
\@writefile{toc}{\contentsline {subsection}{\tocsubsection {}{4.4}{Independence of twisting choice}}{44}}
\newlabel{gw-ind-twisting}{{4.4.1}{44}}
\newlabel{twist-compat-obs}{{4.4.2}{44}}
\citation{Abramovich-Vistoli}
\citation{Costello}
\citation{Costello}
\citation{ACW}
\citation{Behrend-Fantechi}
\citation{degrev2}
\citation{Li2}
\citation{degrev2}
\@writefile{toc}{\contentsline {subsection}{\tocsubsection {}{4.5}{Invariance under twisting}}{46}}
\newlabel{definv}{{4.6}{46}}
\@writefile{toc}{\contentsline {subsection}{\tocsubsection {}{4.6}{Deformation invariance}}{46}}
\newlabel{T:definv}{{4.6.1}{46}}
\newlabel{deg-comp-li}{{4.7}{46}}
\@writefile{toc}{\contentsline {subsection}{\tocsubsection {}{4.7}{Comparison with Jun Li's invariants}}{46}}
\newlabel{C:compare-Li}{{4.7.1}{46}}
\citation{M-P}
\@writefile{toc}{\contentsline {subsubsection}{\tocsubsubsection {}{4.7.2}{}}{47}}
\@writefile{toc}{\contentsline {subsubsection}{\tocsubsubsection {}{4.7.3}{}}{47}}
\@writefile{toc}{\contentsline {subsubsection}{\tocsubsubsection {}{4.7.4}{}}{47}}
\@writefile{toc}{\contentsline {subsubsection}{\tocsubsubsection {}{4.7.5}{}}{47}}
\newlabel{SS:disconnected-maps}{{4.8}{47}}
\@writefile{toc}{\contentsline {subsection}{\tocsubsection {}{4.8}{Disconnected maps and invariants}}{47}}
\newlabel{D:modular-graph}{{4.8.1}{47}}
\citation{Abramovich-Vistoli}
\citation{Abramovich-Vistoli}
\citation{Abramovich-Vistoli}
\@writefile{toc}{\contentsline {subsubsection}{\tocsubsubsection {}{4.8.2}{Moduli stacks and their properties}}{48}}
\@writefile{toc}{\contentsline {subsubsection}{\tocsubsubsection {}{4.8.3}{Disconnected Gromov--Witten invariants}}{48}}
\@writefile{toc}{\contentsline {subsubsection}{\tocsubsubsection {}{4.8.4}{Contraction morphisms}}{48}}
\citation{Costello}
\newlabel{P:disc-compare}{{4.8.5}{49}}
\@writefile{toc}{\contentsline {subsubsection}{\tocsubsubsection {}{4.8.7}{An auxiliary stack of expansions}}{49}}
\citation{Costello}
\citation{ACW}
\citation{Costello}
\@writefile{toc}{\contentsline {section}{\tocsection {}{5}{Degeneration formula}}{51}}
\newlabel{S:Degeneration}{{5}{51}}
\@writefile{toc}{\contentsline {subsection}{\tocsubsection {}{5.1}{Setup}}{51}}
\newlabel{D:enh-spl}{{5.1.1}{52}}
\newlabel{SS:Degeneration}{{5.2}{53}}
\@writefile{toc}{\contentsline {subsection}{\tocsubsection {}{5.2}{Statement of the formula}}{53}}
\newlabel{T:degeneration}{{5.2.1}{53}}
\citation{Li2}
\citation{Li1}
\citation{Li2}
\citation{AGV}
\citation{Chen-Ruan}
\newlabel{S:pf-mainth}{{5.2.3}{54}}
\@writefile{toc}{\contentsline {subsubsection}{\tocsubsubsection {}{5.2.3}{The Chen--Ruan pairing and Theorem 0.4.1\hbox {}}}{54}}
\@writefile{toc}{\contentsline {subsection}{\tocsubsection {}{5.3}{Outline of proof of Theorem 5.2.1\hbox {}}}{55}}
\citation{Costello}
\citation{Costello}
\citation{Manolache}
\citation{Costello}
\citation{Manolache}
\newlabel{Sec:split-coarse}{{5.4}{56}}
\@writefile{toc}{\contentsline {subsection}{\tocsubsection {}{5.4}{Splitting the coarse target}}{56}}
\newlabel{L:coarse-split}{{5.4.1}{56}}
\newlabel{Sec:split-stack-target}{{5.5}{56}}
\@writefile{toc}{\contentsline {subsection}{\tocsubsection {}{5.5}{Splitting the stack target}}{56}}
\newlabel{Lem:split-target-r}{{5.5.1}{57}}
\newlabel{Sec:decompose-moduli}{{5.6}{57}}
\@writefile{toc}{\contentsline {subsection}{\tocsubsection {}{5.6}{Decomposing the moduli space with split target}}{57}}
\newlabel{L:virt-split}{{5.6.1}{58}}
\newlabel{Sec:gluing-target}{{5.7}{58}}
\@writefile{toc}{\contentsline {subsection}{\tocsubsection {}{5.7}{Gluing the target}}{58}}
\citation{AGV}
\newlabel{Lem:glue-target}{{5.7.2}{59}}
\newlabel{Sec:gluing-source}{{5.8}{59}}
\@writefile{toc}{\contentsline {subsection}{\tocsubsection {}{5.8}{Gluing the source}}{59}}
\citation{Behrend-Fantechi}
\newlabel{P:vir-glue-tw}{{5.8.1}{60}}
\citation{AGV}
\citation{ACW}
\newlabel{Sec:coarse-diagonal}{{5.9}{62}}
\@writefile{toc}{\contentsline {subsection}{\tocsubsection {}{5.9}{Comparison with $\Delta $}}{62}}
\newlabel{P:diag-gysin}{{5.9.1}{62}}
\newlabel{C:glue-virt}{{5.9.2}{62}}
\newlabel{SS:endpf}{{5.10}{63}}
\@writefile{toc}{\contentsline {subsection}{\tocsubsection {}{5.10}{End of proof}}{63}}
\citation{ACW}
\@writefile{toc}{\contentsline {section}{\tocsection {Appendix}{A}{Pairs and nodes}}{64}}
\newlabel{A:pairs}{{A}{64}}
\newlabel{onpairs}{{A.1}{64}}
\@writefile{toc}{\contentsline {subsection}{\tocsubsection {}{A.1}{Smooth and locally smooth pairs}}{64}}
\citation{Kato}
\newlabel{logsmpair}{{A.2}{65}}
\@writefile{toc}{\contentsline {subsection}{\tocsubsection {}{A.2}{Transversality for nodal singularities and pairs}}{65}}
\citation{AGV}
\citation{Abramovich-Vistoli}
\newlabel{L:tr-open}{{A.2.2}{66}}
\newlabel{SS:1st-order-sm}{{A.3}{66}}
\@writefile{toc}{\contentsline {subsection}{\tocsubsection {}{A.3}{First-order smoothability of nodal singularities}}{66}}
\@writefile{toc}{\contentsline {section}{\tocsection {Appendix}{B}{Stack constructions}}{66}}
\newlabel{A:stacks}{{B}{66}}
\newlabel{2stacks_as_stacks}{{B.1}{66}}
\@writefile{toc}{\contentsline {subsection}{\tocsubsection {}{B.1}{Using $2$-stacks to define stacks}}{66}}
\citation{Olsson-hom}
\citation{Abramovich-Vistoli}
\newlabel{sepdiag}{{B.1.1}{67}}
\newlabel{rigid_liftings}{{B.1.2}{67}}
\newlabel{rigid_liftings}{{B.1.3}{67}}
\@writefile{toc}{\contentsline {subsection}{\tocsubsection {}{B.2}{Constructing moduli over a base stack}}{67}}
\newlabel{Lem:stack-over-stack}{{B.2.1}{68}}
\@writefile{toc}{\contentsline {subsection}{\tocsubsection {}{B.3}{Inertia stacks of various flavors}}{68}}
\newlabel{SS:inertia}{{B.3.1}{68}}
\@writefile{toc}{\contentsline {subsubsection}{\tocsubsubsection {}{B.3.1}{The inertia stack}}{68}}
\citation{AGV}
\citation{AGV}
\citation{Olsson-cc}
\citation{Aoki-def}
\citation{Olsson-cc}
\citation{Laszlo-Olsson}
\@writefile{toc}{\contentsline {subsubsection}{\tocsubsubsection {}{B.3.2}{Inertia of Deligne--Mumford stacks}}{69}}
\@writefile{toc}{\contentsline {subsubsection}{\tocsubsubsection {}{B.3.3}{Rigidified inertia}}{69}}
\@writefile{toc}{\contentsline {subsubsection}{\tocsubsubsection {}{B.3.4}{Cyclotomic inertia and rigidified inertia}}{69}}
\@writefile{toc}{\contentsline {subsection}{\tocsubsection {}{B.4}{Deformations and obstructions for Artin stacks}}{69}}
\citation{Olsson-log-cotangent}
\@writefile{toc}{\contentsline {section}{\tocsection {Appendix}{C}{Stacks of maps and their obstruction theory}}{70}}
\newlabel{obs_th}{{C}{70}}
\@writefile{toc}{\contentsline {subsection}{\tocsubsection {}{C.1}{Stacks of maps}}{70}}
\citation{Olsson-hom}
\newlabel{flsp}{{C.1.1}{71}}
\newlabel{strepmap}{{C.1.2}{71}}
\newlabel{strepmapalg}{{C.1.5}{71}}
\newlabel{N:fK}{{C.1.6}{71}}
\newlabel{fKbasechange}{{C.1.7}{71}}
\@writefile{toc}{\contentsline {subsubsection}{\tocsubsubsection {}{C.1.7}{Base change}}{71}}
\citation{Abramovich-Vistoli}
\citation{Noseda}
\newlabel{fKpropermap}{{C.1.8}{72}}
\@writefile{toc}{\contentsline {subsubsection}{\tocsubsubsection {}{C.1.8}{Change of family}}{72}}
\newlabel{SS:obs-th}{{C.2}{72}}
\@writefile{toc}{\contentsline {subsection}{\tocsubsection {}{C.2}{Obstruction theory on stacks of maps}}{72}}
\citation{Olsson-cc}
\citation{LN07}
\citation{Behrend-Fantechi}
\citation{ACW}
\newlabel{obsth}{{C.2.1}{73}}
\citation{Illusie}
\citation{Laudal}
\citation{Ran-pairs}
\citation{Illusie}
\@writefile{toc}{\contentsline {subsection}{\tocsubsection {}{C.3}{Perfect amplitude}}{74}}
\newlabel{itsperf}{{C.3.3}{74}}
\bibcite{Cime}{A}
\bibcite{ACFW}{ACFW}
\bibcite{ACV}{ACV}
\bibcite{ACW}{ACW}
\bibcite{degrev2}{AF}
\bibcite{AGV}{AGV}
\bibcite{AJ}{AJ}
\bibcite{AOV-maps}{AOV}
\bibcite{Abramovich-Vistoli}{AV}
\bibcite{Alexander-Hirschowitz}{AH}
\bibcite{AG}{AG}
\bibcite{Aoki-def}{Ao}
\bibcite{BayerManin}{BM}
\bibcite{Behrend-Fantechi}{BF}
\bibcite{Bernstein}{Ber}
\bibcite{Borne-Vistoli}{BV}
\bibcite{Cadman1}{C1}
\@writefile{toc}{\contentsline {section}{\tocsection {Appendix}{}{References}}{75}}
\bibcite{Caporaso-Harris}{CH}
\bibcite{Chen-Ruan}{CR}
\bibcite{Costello}{Co}
\bibcite{Cox-Katz}{C-K}
\bibcite{Gathmann}{Ga}
\bibcite{Graber-Vakil}{GV}
\bibcite{Harris-Mumford}{HM}
\bibcite{Hirschowitz}{Hi}
\bibcite{Illusie}{Il}
\bibcite{Ionel-Parker1}{IP1}
\bibcite{Ionel-Parker2}{IP2}
\bibcite{Kato}{Ka}
\bibcite{Kim}{Ki}
\bibcite{KKO}{KKO}
\bibcite{Kim-Kresch-Pantev}{KKP}
\bibcite{Kim-Sato}{KS}
\bibcite{Laszlo-Olsson}{LO}
\bibcite{Laudal}{La}
\bibcite{L-MB}{LMB}
\bibcite{Li-Ruan}{LR}
\bibcite{Li1}{Li1}
\bibcite{Li2}{Li2}
\bibcite{LN07}{LN}
\bibcite{Manolache}{Ma}
\bibcite{Matsuki-Olsson}{M-O}
\bibcite{M-P}{MP}
\bibcite{Mochizuki}{Mo}
\bibcite{Noseda}{No}
\bibcite{Olsson-log-stacks}{Ol03}
\bibcite{Olsson-log-cotangent}{Ol05}
\bibcite{Olsson-hom}{Ol06}
\bibcite{Olsson-twisted}{Ol07a}
\bibcite{Olsson-cc}{Ol07b}
\bibcite{OlssonPisa}{Ol08}
\bibcite{Ran}{Ra87}
\bibcite{Ran-pairs}{Ra89}
\bibcite{Spaltenstein}{Sp}
\bibcite{Vakil}{Va}
\newlabel{tocindent-1}{0pt}
\newlabel{tocindent0}{68.86317pt}
\newlabel{tocindent1}{77.8367pt}
\newlabel{tocindent2}{0pt}
\newlabel{tocindent3}{0pt}
\@writefile{toc}{\contentsline {section}{\tocsection {Appendix}{D}{Things to do}}{78}}