\begin{thebibliography}{BCNWS14}

\bibitem[AV14]{AmerVerb}
Ekaterina Amerik and Misha Verbitsky.
\newblock Morrison-{K}awamata cone conjecture for hyperkahler manifolds, 2014.
\newblock arXiv:1408.3892.

\bibitem[Bak13]{Bakker}
Benjamin Bakker.
\newblock A classification of extremal {L}angrangian planes in holomorphic
  symplectic varieties, 2013.
\newblock arXiv:1310.6341.

\bibitem[BCNWS14]{BCNWS}
Samuel Boissi\`ere, Andrea Cattaneo, Marc Nieper-Wisskirchen, and Alessandra
  Sarti.
\newblock The automorphism group of the {H}ilbert scheme of two points on a
  generic projective {$K3$} surface, 2014.
\newblock arXiv:1410.8387.

\bibitem[BHT13]{BHT}
Arend Bayer, Brendan Hassett, and Yuri Tschinkel.
\newblock Mori cones of holomorphic symplectic varieties of {$K3$} type.
\newblock {\em Annales scientifiques de l'\'Ecole normale sup\'erieure}, to
  appear, 2013.
\newblock arXiv:1307:2291.

\bibitem[BJ14]{BJ}
Benjamin Bakker and Andrei Jorza.
\newblock Lagrangian 4-planes in holomorphic symplectic varieties of
  {$\text{K3}^{[4]}$}-type.
\newblock {\em Cent. Eur. J. Math.}, 12(7):952--975, 2014.

\bibitem[BM14a]{BM2}
Arend Bayer and Emanuele Macr{\`{\i}}.
\newblock M{MP} for moduli of sheaves on {K}3s via wall-crossing: nef and
  movable cones, {L}agrangian fibrations.
\newblock {\em Invent. Math.}, 198(3):505--590, 2014.

\bibitem[BM14b]{BM1}
Arend Bayer and Emanuele Macr{\`{\i}}.
\newblock Projectivity and birational geometry of {B}ridgeland moduli spaces.
\newblock {\em J. Amer. Math. Soc.}, 27(3):707--752, 2014.

\bibitem[Eic74]{Eichler}
Martin Eichler.
\newblock {\em Quadratische {F}ormen und orthogonale {G}ruppen}.
\newblock Springer-Verlag, Berlin, 1974.
\newblock Zweite Auflage, Die Grundlehren der mathematischen Wissenschaften,
  Band 63.

\bibitem[GHS10]{GHS}
V.~Gritsenko, K.~Hulek, and G.~K. Sankaran.
\newblock Moduli spaces of irreducible symplectic manifolds.
\newblock {\em Compos. Math.}, 146(2):404--434, 2010.

\bibitem[HHT12]{HHT3}
David Harvey, Brendan Hassett, and Yuri Tschinkel.
\newblock Characterizing projective spaces on deformations of {H}ilbert schemes
  of {K}3 surfaces.
\newblock {\em Comm. Pure Appl. Math.}, 65(2):264--286, 2012.

\bibitem[HT09]{HT2}
Brendan Hassett and Yuri Tschinkel.
\newblock Moving and ample cones of holomorphic symplectic fourfolds.
\newblock {\em Geom. Funct. Anal.}, 19(4):1065--1080, 2009.

\bibitem[HT10a]{HTJus}
Brendan Hassett and Yuri Tschinkel.
\newblock Flops on holomorphic symplectic fourfolds and determinantal cubic
  hypersurfaces.
\newblock {\em J. Inst. Math. Jussieu}, 9(1):125--153, 2010.

\bibitem[HT10b]{HT4}
Brendan Hassett and Yuri Tschinkel.
\newblock Intersection numbers of extremal rays on holomorphic symplectic
  varieties.
\newblock {\em Asian J. Math.}, 14(3):303--322, 2010.

\bibitem[Huy99]{HuyBasic}
Daniel Huybrechts.
\newblock Compact hyper-{K}\"ahler manifolds: basic results.
\newblock {\em Invent. Math.}, 135(1):63--113, 1999.

\bibitem[Huy11]{huy}
Daniel Huybrechts.
\newblock A global {T}orelli theorem for hyperk\"ahler manifolds (after
  {M}.~{V}erbitsky), 2011.
\newblock S{\'e}minaire Bourbaki. Vol. 2010/2011, Exp. No. 1040.

\bibitem[HVA13]{HVA}
Brendan Hassett and Anthony V{\'a}rilly-Alvarado.
\newblock Failure of the {H}asse principle on general {$K3$} surfaces.
\newblock {\em J. Inst. Math. Jussieu}, 12(4):853--877, 2013.

\bibitem[HVAV11]{HVAV}
Brendan Hassett, Anthony V{\'a}rilly-Alvarado, and Patrick Varilly.
\newblock Transcendental obstructions to weak approximation on general {K}3
  surfaces.
\newblock {\em Adv. Math.}, 228(3):1377--1404, 2011.

\bibitem[HW60]{HW}
G.~H. Hardy and E.~M. Wright.
\newblock {\em An introduction to the theory of numbers}.
\newblock The Clarendon Press Oxford University Press, London, fourth edition,
  1960.

\bibitem[Mar08]{MarkJAG}
Eyal Markman.
\newblock On the monodromy of moduli spaces of sheaves on {$K3$} surfaces.
\newblock {\em J. Algebraic Geom.}, 17(1):29--99, 2008.

\bibitem[Mar11]{MarkSurv}
Eyal Markman.
\newblock A survey of {T}orelli and monodromy results for
  holomorphic-symplectic varieties.
\newblock In {\em Complex and differential geometry}, volume~8 of {\em Springer
  Proc. Math.}, pages 257--322. Springer, Heidelberg, 2011.

\bibitem[MSTVA14]{McKSaTaVA}
Kelly McKinnie, Justin Sawon, Sho Tanimoto, and Anthony V\'arilly-Alvarado.
\newblock Brauer groups on {$K3$} surfaces and arithmetic applications, 2014.
\newblock arXiv:1404.5460.

\bibitem[Muk06]{MukaiGenus13}
Shigeru Mukai.
\newblock Polarized {$K3$} surfaces of genus thirteen.
\newblock In {\em Moduli spaces and arithmetic geometry}, volume~45 of {\em
  Adv. Stud. Pure Math.}, pages 315--326. Math. Soc. Japan, Tokyo, 2006.

\bibitem[MY14]{MarkYosh}
Eyal Markman and Kota Yoshioka.
\newblock A proof of the {K}awamata-{M}orrison conjecture for holomorphic
  symplectic varieties of ${K}3^{[n]}$ or generalized {K}ummer deformation
  type, 2014.
\newblock arXiv:1402.2049.

\bibitem[O'G99]{ogrady}
Kieran~G. O'Grady.
\newblock Desingularized moduli spaces of sheaves on a {$K3$}.
\newblock {\em J. Reine Angew. Math.}, 512:49--117, 1999.

\bibitem[Ogu14]{oguiso}
K.~Oguiso.
\newblock Some aspects of explicit birational geometry inspired by complex
  dynamics, 2014.
\newblock arXiv:1404.2982.

\bibitem[SD74]{SD}
B.~Saint-Donat.
\newblock Projective models of {$K-3$} surfaces.
\newblock {\em Amer. J. Math.}, 96:602--639, 1974.

\bibitem[Ver13]{verb}
Misha Verbitsky.
\newblock Mapping class group and a global {T}orelli theorem for hyperkahler
  manifolds.
\newblock {\em Duke Mathematical Journal}, 162(15):2929--2986, 2013.
\newblock arXiv:0908.4121.

\bibitem[Yos12]{Yosh}
Kota Yoshioka.
\newblock Bridgeland's stability and the positive cone of the moduli spaces of
  stable objects on an abelian surface, 2012.
\newblock arXiv:1206.4838.

\end{thebibliography}