\begin{thebibliography}{10} \bibitem{AK} A.~B. Altman and S.~L. Kleiman. \newblock Foundations of the theory of {F}ano schemes. \newblock {\em Compositio Math.}, 34(1):3--47, 1977. \bibitem{AV} E.~Amerik and C.~Voisin. \newblock Potential density of rational points on the variety of lines of a cubic fourfold. \newblock {\em Duke Math. J.}, 145(2):379--408, 2008. \bibitem{ACGH} E.~Arbarello, M.~Cornalba, P.~A. Griffiths, and J.~Harris. \newblock {\em Geometry of algebraic curves. {V}ol. {I}}, volume 267 of {\em Grundlehren der Mathematischen Wissenschaften}. \newblock Springer-Verlag, New York, 1985. \bibitem{Bea85} A.~Beauville. \newblock Vari\'et\'es k\"ahl\'eriennes compactes avec {$c\sb 1=0$}. \newblock {\em Ast\'erisque}, (126):181--192, 1985. \newblock Geometry of $K3$ surfaces: moduli and periods (Palaiseau, 1981/1982). \bibitem{Beau99} A.~Beauville. \newblock Determinantal hypersurfaces. \newblock {\em Michigan Math. J.}, 48:39--64, 2000. \newblock Dedicated to William Fulton on the occasion of his 60th birthday. \bibitem{BeauDonagi} A.~Beauville and R.~Donagi. \newblock La vari\'et\'e des droites d'une hypersurface cubique de dimension {$4$}. \newblock {\em C. R. Acad. Sci. Paris S\'er. I Math.}, 301(14):703--706, 1985. \bibitem{Boucksom} S.~Boucksom. \newblock Le c\^one k\"ahl\'erien d'une vari\'et\'e hyperk\"ahl\'erienne. \newblock {\em C. R. Acad. Sci. Paris S\'er. I Math.}, 333(10):935--938, 2001. \bibitem{BK} A.~Buckley and T.~Ko{\v{s}}ir. \newblock Determinantal representations of smooth cubic surfaces. \newblock {\em Geom. Dedicata}, 125:115--140, 2007. \bibitem{BHL} D.~Burns, Y.~Hu, and T.~Luo. \newblock Hyper{K}\"ahler manifolds and birational transformations in dimension 4. \newblock In {\em Vector bundles and representation theory (Columbia, MO, 2002)}, volume 322 of {\em Contemp. Math.}, pages 141--149. Amer. Math. Soc., Providence, RI, 2003. \bibitem{Clebs} A.~Clebsch. \newblock Die {G}eometrie auf den {F}l\"achen dritter {O}rdnung. \newblock {\em J. Reine Angew. Math.}, 65:359--380, 1866. \bibitem{CG} C.~H. Clemens and P.~A. Griffiths. \newblock The intermediate {J}acobian of the cubic threefold. \newblock {\em Ann. of Math. (2)}, 95:281--356, 1972. \bibitem{CLSS} D.~F. Coray, D.~J. Lewis, N.~I. Shepherd-Barron, and P.~Swinnerton-Dyer. \newblock Cubic threefolds with six double points. \newblock In {\em Number theory in progress, Vol. 1 (Zakopane-Ko\'scielisko, 1997)}, pages 63--74. de Gruyter, Berlin, 1999. \bibitem{Cr} L.~Cremona. \newblock Ueber die {P}olar-{H}exaeder bei den {F}l\"achen dritter ordnung. \newblock {\em Math. Ann.}, 13(2):301--304, 1878. \newblock Reprinted in {\em Opere}, t. 3, pp. 430-433. \bibitem{Deb} O.~Debarre. \newblock Un contre-exemple au th\'eor\`eme de {T}orelli pour les vari\'et\'es symplectiques irr\'eductibles. \newblock {\em C. R. Acad. Sci. Paris S\'er. I Math.}, 299(14):681--684, 1984. \bibitem{Dickson} L.~E. Dickson. \newblock Algebraic {T}heory of the {E}xpressibility of {C}ubic {F}orms as {D}eterminants, with {A}pplication to {D}iophantine {A}nalysis. \newblock {\em Amer. J. Math.}, 43(2):102--125, 1921. \bibitem{Dolg} I.~V. Dolgachev. \newblock Luigi {C}remona and cubic surfaces. \newblock In {\em Luigi Cremona (1830--1903) (Italian)}, volume~36 of {\em Incontr. Studio}, pages 55--70. Istituto Lombardo di Scienze e Lettere, Milan, 2005. \bibitem{Fr} M.~J. Fryers. \newblock The movable fan of the {H}orrocks-{M}umford quintic, 2001. \newblock {\tt http://arXiv.org/abs/math/0102055}. \bibitem{Fujiki} A.~Fujiki. \newblock On the de {R}ham cohomology group of a compact {K}\"ahler symplectic manifold. \newblock In {\em Algebraic geometry, Sendai, 1985}, volume~10 of {\em Adv. Stud. Pure Math.}, pages 105--165. North-Holland, Amsterdam, 1987. \bibitem{Fulton} W.~Fulton. \newblock {\em Intersection theory}, volume~2 of {\em Ergebnisse der Mathematik und ihrer Grenzgebiete (3) [Results in Mathematics and Related Areas (3)]}. \newblock Springer-Verlag, Berlin, 1984. \bibitem{Grass} H.~Grassmann. \newblock Die stereometrischen {G}leichungen dritten {G}rades, und die dadurch erzeugten {O}berfl\"achen. \newblock {\em J. Reine Angew. Math.}, 49:47--65, 1855. \bibitem{Has00} B.~Hassett. \newblock Special cubic fourfolds. \newblock {\em Compositio Math.}, 120(1):1--23, 2000. \bibitem{HT01} B.~Hassett and Y.~Tschinkel. \newblock Rational curves on holomorphic symplectic fourfolds. \newblock {\em Geom. Funct. Anal.}, 11(6):1201--1228, 2001. \bibitem{HT07} B.~Hassett and Y.~Tschinkel. \newblock Moving and ample cones of holomorphic symplectic fourfolds. \newblock {\em Geom. Funct. Anal.}, to appear. \bibitem{Hu} B.~Hunt. \newblock {\em The geometry of some special arithmetic quotients}, volume 1637 of {\em Lecture Notes in Mathematics}. \newblock Springer-Verlag, Berlin, 1996. \bibitem{Hu97} D.~Huybrechts. \newblock Birational symplectic manifolds and their deformations. \newblock {\em J. Differential Geom.}, 45(3):488--513, 1997. \bibitem{Hu99} D.~Huybrechts. \newblock Compact hyper-{K}\"ahler manifolds: basic results. \newblock {\em Invent. Math.}, 135(1):63--113, 1999. \bibitem{Kap} M.~M. Kapranov. \newblock Chow quotients of {G}rassmannians {I}. \newblock In {\em I.M. Gelfand Seminar}, volume~16 of {\em Adv. Soviet Math.}, pages 29--110. Amer. Math. Soc., Providence, 1993. \bibitem{Kap2} M.~M. Kapranov. \newblock Veronese curves and {G}rothendieck-{K}nudsen moduli space $\overline {M}\sb {0,n}$. \newblock {\em J. Algebraic Geom.}, 2(2):239--262, 1993. \bibitem{Kaw} Y.~Kawamata. \newblock On the cone of divisors of {C}alabi-{Y}au fiber spaces. \newblock {\em Internat. J. Math.}, 8(5):665--687, 1997. \bibitem{Leung} N.~C. Leung. \newblock Lagrangian submanifolds in hyper{K}\"ahler manifolds, {L}egendre transformation. \newblock {\em J. Differential Geom.}, 61(1):107--145, 2002. \bibitem{LP} E.~Looijenga and C.~Peters. \newblock Torelli theorems for {K}\"ahler {$K3$} surfaces. \newblock {\em Compositio Math.}, 42(2):145--186, 1980/81. \bibitem{Mar06} E.~Markman. \newblock Integral constraints on the monodromy group of the hyperkahler resolution of a symmetric product of a {K3} surface. \newblock arXiv:math/0601304v3. \bibitem{Mor} D.~R. Morrison. \newblock Compactifications of moduli spaces inspired by mirror symmetry. \newblock {\em Ast\'erisque}, 218:243--271, 1993. \newblock Journ\'ees de G\'eom\'etrie Alg\'ebrique d'Orsay (Orsay, 1992). \bibitem{Mu84} S.~Mukai. \newblock Symplectic structure of the moduli space of sheaves on an abelian or {$K3$} surface. \newblock {\em Invent. Math.}, 77(1):101--116, 1984. \bibitem{Nami2} Y.~Namikawa. \newblock Counter-example to global {T}orelli problem for irreducible symplectic manifolds. \newblock {\em Math. Ann.}, 324(4):841--845, 2002. \bibitem{Reid} M.~Reid. \newblock Minimal models of canonical {$3$}-folds. \newblock In {\em Algebraic varieties and analytic varieties (Tokyo, 1981)}, volume~1 of {\em Adv. Stud. Pure Math.}, pages 131--180. North-Holland, Amsterdam, 1983. \bibitem{Schr} H.~E. Schr\"oter. \newblock Nachweis der 27 {G}eraden auf der allgemeinen {O}berfl\"achen dritter {O}rdnung. \newblock {\em J. Reine Angew. Math.}, 62:265--280, 1863. \bibitem{BSegre} B.~Segre. \newblock On the rational solutions of homogeneous cubic equations in four variables. \newblock {\em Math. Notae}, 11:1--68, 1951. \bibitem{Segre} C.~Segre. \newblock Sulle variet\`a cubiche dello spazio a quattro dimensioni e su certi sistemi di rette e certe superficie dello spazio ordinario. \newblock {\em Memorie della Reale Accademia delle Scienze di Torino}, XXXIX:3--48, 1887. \newblock Reprinted in `Opere. Vol. IV.' by the {U}nione {M}atematica {I}taliana, Edizioni Cremonese, Rome, 1963. \bibitem{WW} J.~Wierzba and J.~A. Wi{\'s}niewski. \newblock Small contractions of symplectic 4-folds. \newblock {\em Duke Math. J.}, 120(1):65--95, 2003. \end{thebibliography}