Deforming Calabi-Yau threefolds

Mathematische Annalen

Volumn 308, Issue 2, 1997, Pages 187-220

  Gross, Mark ^a  

^a Department of Population Medicine and Diagnostic Sciences   (United States)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 0031500790     PISSN: 00255831     EISSN: None     Source Type: Journal    
DOI: 10.1007/s002080050072     Document Type: Article

References (51)

1. Alonso, L., Jeremías, A., Lipman, J.: Local Homology and Cohomology. Preprint, 1995.
2. Altmann, K.: The Versal Deformation of an Isolated Toric Gorenstein Singularity. Preprint (1994).
3. Buchsbaum, D., Eisenbud, D.: Algebra Structures for Finite Free Resolutions and Some Structure Theorems for Ideals of Codimension 3. Amer. J. Math. 99, (1977) 447-485.
4. Deligne, P.: Théorème de Lefschetz et Critères de dégénérescence de Suites Spectrales. Inst. Hautes. Études Sci., Publ. Math. 35 (1968), 197-226.
5. Dolgachev, I., Ortland, O.: Point Sets in Projective Space and Theta Functions. Astérisque 165 (1988).
6. Douady, A.: Le Probleme des Modules Locaux pour les Espaces C-Analytiques Compacts. Ann. scient. Éc. Norm. Sup. 4e série, 7, (1974) 569-602.
7. Friedman, R.: Global Smoothings of Varieties with Normal Crossings. Annals of Math. 118 (1983), 75-114.
8. Friedman, R.: Simultaneous Resolution of Threefold Double Points. Math. Ann. 274, (1986) 671-689.
9. Grauert, H.: Über Modifikationen und Exzeptionelle Analytische Mengen. Math. Ann. 146 (1962), 331-368.
10. Grauert, H.: Der Satz von Kuranishi für Kompakte Komplexe Räume. Invent. Math. 25, (1974) 107-142.
11. Gross, M.: The Deformation Space of Calabi-Yau n-folds with Canonical Singularities can be Obstructed. To appear in Essays in Mirror Symmetry, II, edited by B. Greene.
12. Gross, M.: Primitive Calabi-Yau Threefolds. To appear in J. Diff. Geom.
13. Grothendieck, A., Local Cohomology. (Notes by R. Hartshorne), LNM 41. Berlin, Heidelberg: Springer 1967
14. Grothendieck, A., Dieudonné, J., EGA IV. Étude locale des schémas et des morphismes des schémas Publ. Math. IHES 20 (1964).
15. Hartshorne, R., Residues and Duality. LNM 20. Berlin, Heidelberg: Springer 1966.
16. Hartshorne, R., Algebraic Geometry. Berlin, Heidelberg: Springer 1977.
17. Kawamata, Y.: Minimal Models and the Kodaira Dimension of Algebraic Fiber Spaces. J. Reine Angew. Math, 363, (1985) 1-46.
18. Kawamata, Y.: Unobstructed Deformations - A Remark on a Paper of Z. Ran. J. Algebraic Geometry 1, (1992) 183-190.
19. Kawamata, Y.: Unobstructed Deformations II. J. Algebraic Geometry 3, (1995) 277-280.
20. Kawamata, Y., Matsuda, K., Matsuki, K.: Introduction to the Minimal Model Program. Algebraic Geometry, Sendai, Adv. Stud. Pure Math. 10, 283-360. Kinokuniya-North-Holland, 1987
21. Kleiman, S.: The Enumerative Theory of Singularities. Real and Complex Singularities, Oslo, 1976, (P. Holm, ed.), Sijthoff+Noordhoof, (1977) 297-396.
22. Kleppe, H., Laksov, D.: The Algebraic Structure and Deformation of Pfaffian Schemes. J. Algebra 64, (1980) 167-189.
23. Kollár, J., and Mori, S.: Classification of Three-dimensional Flips. J. Amer. Math. Soc., 5, (1992) 533-703.
24. Kollár, J., Shepherd-Barron, N.: Threefolds and Deformations of Surface Singularities. Invent. Math. 91, (1988) 299-338.
25. Lichtenbaum, S., Schlessinger, M.: The Cotangent Complex of a Morphism. Trans. Amer. Math. Soc. 128 (1967), 41-70.
26. Lieberman, D., Rossi, H.: Deformations of Strongly Pseudo-complex Manifolds. Rencontre sur l'Analyse Complexe À Plusieurs Variables et les Systèmes Surdéterminés Les Presses de l'Université de Montréal, (1975) 119-166.
27. Looijenga, E.: The Smoothing Components of a Triangle Singularity. II. Math. Ann. 269, (1984) 357-387.
28. Namikawa, Y.: On Deformations of Calabi-Yau 3-folds with Terminal Singularities. Topology 33 (1994), 429-446.
29. Namikawa, Y.: Stratified Local Moduli of Calabi-Yau 3-folds. Preprint (1995).
30. Namikawa., Y., Steenbrink, J.: Global Smoothing of Calabi-Yau 3-folds. Invent. Math. 122, (1995) 403-419.
31. Ohsawa, T.: A Reduction Theorem for Cohomology Groups of Very Strongly q-Convex Kähler Manifolds. Invent. Math. 63, (1981) 335-354.
32. Ran, Z.: Deformations of Maps. In: Algebraic Curves and Projective Geometry, E. Ballico, C. Ciliberto (Eds) LNM 1389. Berlin, Heidelberg: Springer 1989.
33. Ran, Z.: Deformations of Manifolds with Torsion or Negative Canonical Bundle. J. of Algebraic Geometry 1, (1992) 279-291.
34. Ran, Z.: Deformations of Calabi-Yau Kleinfolds. In Essays in Mirror Symmetry (ed. S.-T. Yau) Int. Press, Hong Kong, (1992) 451-457.
35. Ran, Z.: Lifting of Cohomology and Deformations of Certain Holomorphic Maps. Bull. Amer. Math. Soc. 26, (1992) 113-117.
36. Ran, Z.: Hodge Theory and Deformations of Maps. Preprint.
37. Ran, Z.: Unobstructedness of Calabi-Yau Orbikleinfolds. Preprint (1993).
38. Reid, M.: Canonical 3-folds. Géométrie Algébrique Angers, (A. Beauville, ed.), Sijthoff+Noordhoof, (1980) 273-310.
39. Reid, M.: Non-normal del Pezzo Surfaces. Preprint (1994).
40. Rotman, J., An Introduction to Homological Algebra. New York: Academic Press 1979.
41. Schlessinger, M.: Functors on Artin Rings. Trans. Amer. Math. Soc. 130, (1968), 208-222.
42. Schlessinger, M.: Rigidity of Quotient Singularities. Invent. Math. 14, 17-26, (1971).
43. Steenbrink, J., van Straten, D.: Extendibility of Holomorphic Differential Forms Near Isolated Hypersurface Singularities. Abh. Math. Sem. Univ. Hamburg 55 (1985) 97-110.
44. Teissier, B.: The Hunting of Invariants in the Geometry of Discriminants. Real and Complex Singularities, Oslo, 1976, (P. Holm, ed.), Sijthoff+Noordhoof, (1977) 565-677.
45. Tian, G.: Smoothness of the Universal Deformation Space of Compact Calabi-Yau Manifolds and its Petersson-Weil Metric. In: Mathematical Aspects of String Theory, 629-646, ed. S.-T. Yau, World Scientific, Singapore, 1987.
46. Tian, G.: Smoothing 3-folds with trivial canonical bundle and ordinary double points. In: Essays in Mirror Symmetry, (ed. S.-T. Yau) Int. Press, Hong Kong, (1992) 458-479.
47. Todorov, A.: The Weil-Petersson Geometry of the Moduli Space of SU(n ≥ 3) (Calabi-Yau) Manifolds I. Commun. Math. Phys 126, (1989) 325-346.
48. Wahl, J.: Equisingular Deformations of Normal Surface Singularities, I. Annals of Math., 104 (1976), 325-356.
49. Wahl, J.: Elliptic Deformations of Minimally Elliptic Singularities. Math. Ann. 253, (1980), 241-262.
50. Wilson, P.M.H.: The Kähler Cone on Calabi-Yau Threefolds. Invent. Math. 107, (1992) 561-583.
51. Wilson, P.M.H.: Symplectic Deformations of Calabi-Yau Threefolds. To appear in J. Diff. Geom.