Special Cubic Fourfolds

Compositio Mathematica

Volumn 120, Issue 1, 2000, Pages 1-23

  Hassett, Brendan ^a  

^a UNIVERSITY OF CHICAGO   (United States)

Author keywords

K3 surfaces; Noether Lefschetz loci; Period domains

Indexed keywords

EID: 0039519342     PISSN: 0010437X     EISSN: None     Source Type: Journal    
DOI: 10.1023/A:1001706324425     Document Type: Article

References (31)

1. Altman, A. and Kleiman, S.: Foundations of the theory of Fano schemes, Compositio Math. 34 (1977), 3 47.
2. Baily, W. L. and Borel, A.: Compactifications of arithmetic quotients of bounded symmetric domains, Ann. of Math. 84 (1966), 442-528.
3. Beauville, A.: Variétés kähleriennes dont la première classe de Chern est nulle, J. Differential Geom. 18 (1983), 755-782.
4. Beauville, A.: Surjectivité de l'application des périodes, In: Géométrie des Surfaces K3: Modules et Périodes-Séminaire Palaiseau, Astérisque 126, (1985), 122-128.
5. Beauville, A. and Donagi, R.: La variété des droites d'une hypersurface cubique de dimension 4, C.R. Acad. Sci .Paris, Sér. I 301 (1985), 703-706.
6. Borel, A.: Some metric properties of arithmetic quotients of symmetric spaces and an extension theorem, J. Differential Geom. 6 (1972), 543-560.
7. Clemens, C.H.: Degenerations of Kahler manifolds, Duke Math J. 44 (1977), 215-290.
8. Debarre, O.: Un contre-exemple au théorème de Torelli pour les variétés symplectiques irréductibles, C.R. Acad. Sci. Paris, Sér. 1299 (1984), 681-684.
9. Dolgachev, I.: Integral quadratic forms, in Séminaire Bourbaki Exposé 611, Astérisque 105-106 (1983), 251-275.
10. Fano, G.: Sulle forme cubiche dello spazio a cinque dimensioni contenenti rigate rationali de 4° ordine, Comment. Math. Helv. 15 (1943), 71-80.
11. Gauss, C.F.: Disquisitiones Arithmeticae, Yale University Press, New Haven, 1966.
12. Griffiths, P. and Schmid, W.: Recent developments in Hodge theory, In: International Colloquium on Discrete Subgroups of Lie Groups and Applications to Moduli, Tata Institute of Fundamental Research and Oxford University Press, Bombay, 1973, pp. 31-127.
13. Hassett, B.: Special cubic hypersurfaces of dimension four, Harvard University Thesis, Cambridge, Mass., 1996.
14. Hassett, B.: Some rational cubic fourfolds, to appear in J. Algebraic Geom. (1997).
15. Izadi, E.: A Prym construction for the cohomology of a cubic hypersurface, Preprint in alggeom/9701012. (1997).
16. Loojenga, E. and Peters, C.: Torelli theorem for Kähler K3 surfaces, Compositio Math. 42 (1981), 145-186.
17. 5, Rend. Sem. Mat. Univ. Padova 11 (1940), 108-112.
18. Mumford, D., Fogarty, J., and Kirwan, F.: Geometric Invariant Theory, Springer, Berlin. (1994).
19. Mukai, S.: Symplectic structure of the moduli space of sheaves on an abelian or K3 surface, Invent. Math. 77 (1984), 101-116.
20. Mukai, S.: On the moduli space of bundles on K3 surfaces, I, Vector Bundles on Algebraic Varieties, Proc. Bombay Conference, 1984, Tata Inst. Fund. Res. Stud. 11, Oxford University Press, 1987, pp. 341-413.
21. Mukai, S.: Moduli of vector bundles on K3 surfaces, and symplectic manifolds, Sugaku Expositions 1 (1988), 139-174.
22. Nikulin, V.V.: Integral symmetric bilinear forms and some of their applications, Math. USSR Izvest. 14 (1) (1980), 103-167.
23. Saint-Donat, B.: Projective models of K3 surfaces, Amer. J. Math. 96 (1974), 602-639.
24. Satake, I.: Algebraic Structures of Symmetric Domains, Princeton University Press, Princeton, 1980.
25. Serre, J.P.: A Course in Arithmetic, Springer, New York, 1973.
26. Siu, Y.T.: A simple proof of the surjectivity of the period map of K3 surfaces, Manuscripta Math. 35 (1981), 311-321.
27. Tregub, S.L.: Three constructions of rationality of a cubic fourfold, Moscow Univ. Math. Bull. 39 (3) (1984), 8-16.
28. Tregub, S.L.: Two remarks on four dimensional cubics, Russian Math. Surveys 48 (2) (1993), 206-208.
29. 5, Invent. Math. 86 (1986), 577-601.
30. Zarhin, Y.: Algebraic cycles over cubic fourfolds, Boll. Un. Mat. Ital. B (7), 4b (1990), 833-847.
31. Zucker, S.: The Hodge conjecture for cubic fourfolds, Compositio Math. 34 (1977), 199-209.