This is pdfTeXk, Version 3.141592-1.40.3 (Web2C 7.5.6) (format=pdflatex 2008.11.7) 19 SEP 2010 09:34 entering extended mode %&-line parsing enabled. **deg-revisited (./deg-revisited.tex LaTeX2e <2005/12/01> Babel and hyphenation patterns for english, usenglishmax, dumylang, noh yphenation, arabic, basque, bulgarian, coptic, welsh, czech, slovak, german, ng erman, danish, esperanto, spanish, catalan, galician, estonian, farsi, finnish, french, greek, monogreek, ancientgreek, croatian, hungarian, interlingua, ibyc us, indonesian, icelandic, italian, latin, mongolian, dutch, norsk, polish, por tuguese, pinyin, romanian, russian, slovenian, uppersorbian, serbian, swedish, turkish, ukenglish, ukrainian, loaded. 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(/usr/share/texmf/tex/latex/amsfonts/umsa.fd File: umsa.fd 2002/01/19 v2.2g AMS font definitions ) LaTeX Font Info: Try loading font information for U+msb on input line 14. (/usr/share/texmf/tex/latex/amsfonts/umsb.fd File: umsb.fd 2002/01/19 v2.2g AMS font definitions ) LaTeX Font Info: Try loading font information for U+stmry on input line 14. (/usr/share/texmf/tex/latex/stmaryrd/Ustmry.fd) (./deg-revisited.toc) \tf@toc=\write4 \openout4 = `deg-revisited.toc'. [1{/usr/share/texmf/fonts/map/pdftex/updmap/pdftex.map}] [2] LaTeX Font Warning: Font shape `U/stmry/b/n' undefined (Font) using `U/stmry/m/n' instead on input line 97. [3] LaTeX Font Info: Try loading font information for U+euf on input line 111. (/usr/share/texmf/tex/latex/amsfonts/ueuf.fd File: ueuf.fd 2002/01/19 v2.2g AMS font definitions ) \c@myparagraph=\count121 [4] [5] Overfull \hbox (4.4927pt too wide) in paragraph at lines 209--209 [][]\OT1/cmr/m/n/12 Perhaps the most mys-te-ri-ous part of the for-mula is the fac-tor $[][] \OML/cmm/m/it/12 d[]$\OT1/cmr/m/n/12 . [] [6] [7] Underfull \hbox (badness 10000) in paragraph at lines 271--272 [] Overfull \hbox (13.21794pt too wide) in paragraph at lines 273--289 [][] [] [8] [9] [10] LaTeX Warning: Citation `Aramovich-Vistoli' on page 11 undefined on input line 354. [11] [12] [13] [14] [15] [16] Overfull \hbox (1.25763pt too wide) in paragraph at lines 532--533 \OT1/cmr/m/n/12 1.4.5.\OT1/cmr/m/it/12 Automorphisms.[] []\OT1/cmr/m/n/12 Un-l ike root stacks, twisted nodal stacks do have [] [17] [18] [19] [20] [21] [22] Overfull \hbox (2.8246pt too wide) in paragraph at lines 697--698 \OT1/cmr/m/n/12 2.2.\OT1/cmr/bx/n/12 Twisted ex-panded de-gen-er-a-tions.[] [] \OT1/cmr/m/n/12 We now dis-cuss stacks anal- [] [23] Overfull \hbox (3.62605pt too wide) in paragraph at lines 747--748 [][]\OT1/cmr/m/it/12 The stacks $\U/euf/m/n/12 T[]$ \OT1/cmr/m/it/12 and $\U/eu f/m/n/12 T[]$ \OT1/cmr/m/it/12 are smooth, al-ge-braic con-nected stacks [] Overfull \hbox (35.38087pt too wide) in paragraph at lines 749--750 [][]\OT1/cmr/m/it/12 If $\OML/cmm/m/it/12 Pic\OT1/cmr/m/n/12 (\OML/cmm/m/it/12 D\OT1/cmr/m/n/12 )$ \OT1/cmr/m/it/12 is rep-re-sentable and dis-crete, the ob-j ects of $\U/euf/m/n/12 T[]\OT1/cmr/m/n/12 (\OML/cmm/m/it/12 S\OT1/cmr/m/n/12 )\ OML/cmm/m/it/12 ; \U/euf/m/n/12 T[]\OT1/cmr/m/n/12 (\OML/cmm/m/it/12 S\OT1/cmr/ m/n/12 )$ [] [24] Overfull \hbox (5.72066pt too wide) in paragraph at lines 768--769 [][]\OT1/cmr/m/n/12 An ob-ser-va-tion about the uni-ver-sal fam-ily are use-ful . Let $\OMS/cmsy/m/n/12 W[] ! [] [25] [26] [27] Overfull \hbox (1.244pt too wide) in paragraph at lines 867--869 \OT1/cmr/m/n/12 2.6.\OT1/cmr/bx/n/12 Stable ex-panded con-fig-u-ra-tions.[] [] \OT1/cmr/m/n/12 We now con-sider sta-ble maps [] [28] [29] [30] [31] [32] [33] [34] [35] [36] [37] [38] [39] [40] [41] Overfull \hbox (7.65112pt too wide) in paragraph at lines 1421--1421 \OT1/cmr/m/n/12 4.1.\OT1/cmr/bx/n/12 Curve classes and orb-ifold co-ho-mol-ogy on nodal DM stacks.[] [] [42] [43] Overfull \hbox (12.16917pt too wide) in paragraph at lines 1493--1493 []\OT1/cmr/bx/n/12 Definition 4.3.2. [][]\OT1/cmr/m/n/12 Let $\OML/cmm/m/it/12 m[]; i \OMS/cmsy/m/n/12 2 \OML/cmm/m/it/12 N$ \OT1/cmr/m/n/12 be non-neg-a-tive in-te-gers; $\OML/cmm/m/it/12 ^^M[] \OMS/cmsy/m/n/12 2 \OML/cmm/m/it/12 H[]\OT 1/cmr/m/n/12 (\OML/cmm/m/it/12 X\OT1/cmr/m/n/12 )\OML/cmm/m/it/12 ; i \OMS/cmsy /m/n/12 2 [] [44] [45] [46] Overfull \hbox (5.02538pt too wide) in paragraph at lines 1630--1632 \OT1/cmr/m/n/12 Note that we do not as-sume the graph to be con-nected or even nonempty. [] [47] [48] [49] [50] [51] [52] Underfull \vbox (badness 2285) has occurred while \output is active [] [53] [54] [55] [56] [57] [58] [59] [60] [61] [62] Underfull \vbox (badness 7595) has occurred while \output is active [] [63] [64] Overfull \hbox (16.58163pt too wide) in paragraph at lines 2259--2260 [][]\OT1/cmr/m/n/12 the mor-phism $\OML/cmm/m/it/12 ^^^[]\OT1/cmr/m/n/12 [] \OMS/cmsy/m/n/12 ! \OT1/cmr/m/n/12 []$ in-duces a mor-phism $\OML/cmm/m/it/12 ^^^[]\OT1/cmr/m/n/12 ( []([] \OML/cmm/m/it/12 D[]\OT1/cmr/m/n/12 )) \OMS/cmsy/m/n/12 ! [] [65] [66] [67] [68] Overfull \hbox (4.19775pt too wide) in paragraph at lines 2360--2360 \OT1/cmr/m/n/12 B.3.2.\OT1/cmr/m/it/12 Inertia of Deligne--Mumford stacks.[] [ ]\OT1/cmr/m/n/12 Sup-pose now $\OML/cmm/m/it/12 X$ \OT1/cmr/m/n/12 is a Deligne -- [] Overfull \hbox (2.37111pt too wide) in paragraph at lines 2365--2365 \OT1/cmr/m/n/12 B.3.4.\OT1/cmr/m/it/12 Cyclotomic in-er-tia and rigid-i-fied i n-er-tia.[] []\OT1/cmr/m/n/12 In the the-ory of twisted [] [69] LaTeX Font Info: Try loading font information for OMS+cmr on input line 2389 . (/usr/share/texmf/tex/latex/base/omscmr.fd File: omscmr.fd 1999/05/25 v2.5h Standard LaTeX font definitions ) LaTeX Font Info: Font shape `OMS/cmr/m/n' in size <12> not available (Font) Font shape `OMS/cmsy/m/n' tried instead on input line 2389. [70] [71] [72] [73] Overfull \hbox (1.98637pt too wide) in paragraph at lines 2510--2511 [][]\OT1/cmr/m/n/12 (1) Since $\OML/cmm/m/it/12 W \OMS/cmsy/m/n/12 ! \OML/cmm/m /it/12 T$ \OT1/cmr/m/n/12 and $\OML/cmm/m/it/12 C \OMS/cmsy/m/n/12 ! \U/euf/m/n /12 K$ \OT1/cmr/m/n/12 are l.c.i., both $\U/msb/m/n/12 L[]$ \OT1/cmr/m/n/12 and $\U/msb/m/n/12 L[]$ [] Overfull \hbox (3.05779pt too wide) in paragraph at lines 2512--2514 [][]\OT1/cmr/m/n/12 (2) It is enough to prove that, for each point $\OML/cmm/m/ it/12 x \OMS/cmsy/m/n/12 2 []$\OT1/cmr/m/n/12 , $\OML/cmm/m/it/12 h[]\OT1/cmr/m /n/12 (\OML/cmm/m/it/12 x[]\U/msb/m/n/12 E[]\OT1/cmr/m/n/12 ) = [] [74] [75] Missing character: There is no ï in font cmr10! Missing character: There is no ¿ in font cmr10! Missing character: There is no ½ in font cmr10! Underfull \vbox (badness 10000) has occurred while \output is active [] [76] [77] [78] (./deg-revisited.aux) LaTeX Font Warning: Some font shapes were not available, defaults substituted. 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