A generalization of Griffiths's theorem on rational integrals

Duke Mathematical Journal

Volumn 135, Issue 2, 2006, Pages 303-326

  Dimca, Alexandru ^a   Saito, Morihiko ^b  

^a UNIVERSITÉ DE NICE SOPHIA ANTIPOLIS   (France)

^b KYOTO UNIVERSITY   (Japan)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 33751513726     PISSN: 00127094     EISSN: None     Source Type: Journal    
DOI: 10.1215/S0012-7094-06-13523-8     Document Type: Article

References (43)

1. D. BARLET and M. SAITO, Brieskorn modules and Gauss-Manin systems for non isolated hypersurface singularities, preprint, arXiv:math.CV/0411406
2. A. A. BEǏLINSON, J. BERNSTEIN, and P. DELIGNE, "Faisceaux pervers" in Analysis and Topology on Singular Spaces, I (Luminy, France, 1981), Astérisque 100, Soc. Math. France, Montrouge, 1982, 5-171. MR 0751966
3. E. BRIESKORN, Die Auflösung der rationalen Singularitäten holomorpher Abbildungen, Math. Ann. 178 (1968), 255-270. MR 0233819
4. _, Die Monodromie der isolierten Singularitäten von Hyperfächen, Manuscripta Math. 2 (1970), 103-161. MR 0267607
5. N. BUDUR and M. SAITO, Multiplier ideals, V-filtration, and spectrum, J. Algebraic Geom. 14(2005), 269-282. MR 2123230
6. D. M. BURNS JR. and J. M. WAHL, Local contributions to global deformations of surfaces. Invent. Math. 26 (1974), 67-88. MR 0349675
7. A. D. R. CHOUDARY and A. DTMCA, Koszul complexes and hypersurface singularities, Proc. Amer. Math. Soc. 121 (1994), 1009-1016. MR 1189539
8. P. DELIGNE, Équations différentielles à points singuliers réguliers, Lecture Notes in Math. 163, Springer, Berlin, 1970. MR 0417174
9. _, "Théorie de Hodge, I" in Actes Congrès International des Mathématiciens (Nice, 1970), Tome I, Gauthier-Villars, Paris, 1971, 425-430;
10. II, Inst. Hautes Études Sci. Publ. Math. 40 (1971), 5-57;
11. III, Inst. Hautes Études Sci. Publ. Math. 44 (1974), 5-77. MR0441965; MR 0498551; MR 0498552
12. P. DELIGNE and A. DIMCA, Filtrations de Hodge et par l'ordre du pôle pour les hypersurfaces singulières, Ann. Sci. École Norm. Sup. (4) 23 (1990), 645-656. MR 1072821
13. A. DIMCA, "On the Milnor fibrations of weighted homogeneous polynomials" in Algebraic Geometry (Berlin, 1988), Compositio Math. 76, Kluwer, Dordrecht, 1990, 19-47. MR 1078856
14. _, Singularities and Topology of Hypersurfaces, Universitext, Springer, New York, 1992. MR 1194180
15. _, Hodge numbers of hypersurfaces, Abh. Math, Sem. Univ. Hamburg 66 (1996), 377-386. MR 1418240
16. L. EIN and R. LAZARSFELD, Singularities of theta divisors and the birational geometry of irregular varieties, J. Amer. Math. Soc. 10 (1997), 243-258. MR 1396893
17. M. GORESKY and R. MACPHERSON, Intersection homology theory, Topology 19 (1980), 135-162. MR0572580
18. H. GRAUERT, Ober Modifikationen und exzeptionelle analytische Mengen, Math. Ann. 146 (1962), 331-368. MR 0137127
19. H. GRAUERT and O. RIEMENSCHNEIDER, Verschwindungssätze für analytische Kohomologiegruppen auf komplexen Räumen, Invent. Math. 11 (1970), 263-292. MR 0302938
20. M. GREEN, "Infinitesimal method in Hodge theory" in Algebraic Cycles and Hodge Theory (Torino, Italy, 1993), Lecture Notes in Math. 1594, Springer, Berlin, 1994. 1-92. MR 1335239
21. P. A. GRIFFITHS, On the periods of certain rational integrals, I, II, Ann. of Math. (2) 90 (1969), 460-541. MR 0260733
22. H. A. HAMM, Zür analytischen und algebraichen Beschreibung der Picard-Lefschetz Monodromie, Habilitationsschrift, Georg-August- Universität, Göttingen, Germany, 1974.
23. M. KASHIWARA, B-functions and holonomic systems: Rationality of B-functions, Invent. Math. 38 (1976/77), 33-53. MR 0430304
24. _, "Vanishing cycle sheaves and holonomic systems of differential equations" in Algebraic Geometry (Tokyo/Kyoto, 1982), Lecture Notes in Math. 1016, Springer, Berlin, 1983, 134-142. MR 0726425
25. Y. KAWAMATA, On deformations of compactifiable complex manifolds, Math. Ann. 235 (1978), 247-265. MR 0499279
26. R. LAZARSFELD, Positivity in Algebraic Geometry, II: Positivity for Vector Bundles, and Multiplier Ideals, Ergeb. Math. Grenzgeb. (3) 49, Springer, Berlin, 2004. MR 2095472
27. F. LOESER, Quelques conséquences locales de la théorie de Hodge, Ann. Inst. Fourier (Grenoble) 35 (1985), 75-92. MR 0781779
28. B. MALGRANGE, "Le polynôme de Bernstein d'une singularité isolée" in Fourier Integral Operators and Partial Differential Equations (Nice, 1974), Lecture Notes in Math. 459, Springer, Berlin, 1975, 98 -119. MR 0419827
29. _, "Polynôme de Bernstein-Sato et cohomologie évanescente" in Analysis and Topology on Singular Spaces, II, III (Luminy, France, 1981), Astérisque 101-102, Soc. Math. France, Montrouge, 1983, 243-267. MR 0737934
30. M. MERLE and B. TEISSIER, "Conditions d'adjonction d'après Du Val" in Séminaire sur les Singularités des Surfaces (Palaiseau, France, 1976-1977), Lecture Notes in Math. 777, Springer, Berlin, 1980, 229-247. MR 0579026
31. M. SAITO, Mixed Hodge modules, Publ. Res. Inst. Math. Sci. 26 (1990), 221-333. MR 1047415
32. _, On b-function, spectrum and rational singularity, Math. Ann. 295 (1993), 51-74. MR 1198841
33. _, On microlocal b-function. Bull. Soc. Math. France 122 (1994), 163-184. MR 1273899
34. _, On the Hodge filtration of Hodge modules, preprint, arXiv:math.AG/0504177
35. J. SCHERK and J. H. M. STEENBRINK, On the mixed Hodge structure on the cohomology of the Milnor fibre, Math. Ann. 271 (1985), 641-665. MR 0790119
36. J. H. M. STEENBRINK, Intersection form for quasi-homogeneous singularities, Compositio Math. 34 (1977), 211-223. MR 0453735
37. _, "Mixed Hodge structure on the vanishing cohomology" in Real and Complex Singularities (Oslo, 1976), Sijthoff-Noordhoff, Alphen aan den Rijn, Netherlands, 1977, 525-563. MR 0485870
38. _, Adjunction conditions for 1-forms on surfaces in projective three-space, preprint, arXiv:math.AG/0411405
39. S. USUI, Variation of mixed Hodge structures arising from family of logarithmic deformations, Ann. Sci. École Norm. Sup. (4) 16 (1983), 91-107. MR 0719764
40. M. VAQUIÉ, "Irrégularité des revêtements cycliques" in Singularities (Lille, France, 1991), London Math. Soc. Lecture Note Ser. 201, Cambridge Univ. Press, Cambridge, 1994, 383-419. MR 1295085
41. A. VARČENKO, Asymptotic behavior of holomorphic forms determines a mixed Hodge structure (in Russian), Dokl. Akad. Nauk SSSR 255, no. 5 (1980), 1035-1038;
42. English translation in Soviet Math. Dokl. 22 (1980), 772-775. MR 0597050
43. _, The complex singularity index does not change along the stratum μ = const (in Russian), Funktsional. Anal, i Prilozhen. 16, no. 1 (1982), 1-12, 96. MR 0648803