Monodromy of a family of hypersurfaces containing a given subvariety
Annales scientifiques de l'École Normale Supérieure, Série 4, Tome 38 (2005) no. 3, p. 365-386
@article{ASENS_2005_4_38_3_365_0,
     author = {Otwinowska, Ania and Saito, Morihiko},
     title = {Monodromy of a family of hypersurfaces containing a given subvariety},
     journal = {Annales scientifiques de l'\'Ecole Normale Sup\'erieure},
     publisher = {Elsevier},
     volume = {Ser. 4, 38},
     number = {3},
     year = {2005},
     pages = {365-386},
     doi = {10.1016/j.ansens.2005.03.003},
     zbl = {1086.14010},
     mrnumber = {2166338},
     language = {en},
     url = {http://www.numdam.org/item/ASENS_2005_4_38_3_365_0}
}
Otwinowska, Ania; Saito, Morihiko. Monodromy of a family of hypersurfaces containing a given subvariety. Annales scientifiques de l'École Normale Supérieure, Série 4, Tome 38 (2005) no. 3, pp. 365-386. doi : 10.1016/j.ansens.2005.03.003. https://www.numdam.org/item/ASENS_2005_4_38_3_365_0/

[1] Beilinson A., Bernstein J., Deligne P., Faisceaux pervers, Astérisque, vol. 100, Soc. Math. France, Paris, 1982. | MR 751966 | Zbl 0536.14011

[2] Carlson J., Extensions of mixed Hodge structures, in: Journées de géométrie algébrique d'Angers 1979, Sijthoff-Noordhoff Alphen a/d Rijn, 1980, pp. 107-128. | MR 605338 | Zbl 0471.14003

[3] Clemens H., Degeneration of Kähler manifolds, Duke Math. J. 44 (1977) 215-290. | MR 444662 | Zbl 0353.14005

[4] Deligne P., Théorie de Hodge I, Actes Congrès Intern. Math. 1 (1970) 425-430. | MR 441965 | Zbl 0219.14006

[5] Deligne P., Le formalisme des cycles évanescents, in: SGA7 XIII and XIV, Lecture Notes in Math., vol. 340, Springer, Berlin, 1973, pp. 82-115, and 116-164. | Zbl 0266.14008

[6] Deligne P., La formule de Picard-Lefschetz, in: SGA7 XV, Lecture Notes in Math., vol. 340, Springer, Berlin, 1973, pp. 165-197. | Zbl 0266.14010

[7] Dimca A., Sheaves in Topology, Universitext, Springer, Berlin, 2004. | MR 2050072 | Zbl 1043.14003

[8] Dimca A., Saito M., Monodromy at infinity and the weights of cohomology, Compositio Math. 138 (2003) 55-71. | MR 2002954 | Zbl 1039.32037

[9] Eisenbud D., Commutative Algebra with a View Toward Algebraic Geometry, Springer, New York, 1995. | MR 1322960 | Zbl 0819.13001

[10] Griffiths P., Harris J., On the Noether-Lefschetz theorem and some remarks on codimension two cycles, Math. Ann. 271 (1985) 31-51. | MR 779603 | Zbl 0552.14011

[11] Illusie L., Autour du théorème de monodromie locale, Astérisque 223 (1994) 9-57. | MR 1293970 | Zbl 0837.14013

[12] Katz N., Étude cohomologique des pinceaux de Lefschetz, in: Lecture Notes in Math., vol. 340, Springer, Berlin, 1973, pp. 254-327. | Zbl 0284.14007

[13] Kleiman S., Altman A., Bertini theorems for hypersurface sections containing a subscheme, Comm. Algebra 7 (1979) 775-790. | MR 529493 | Zbl 0401.14002

[14] Lefschetz S., L'analysis situs et la géométrie algébrique, Gauthier-Villars, Paris, 1924. | JFM 50.0663.01

[15] Lewis J.D., A Survey of the Hodge Conjecture, Monograph Series, vol. 10, American Mathematical Society, Providence RI, 1999. | MR 1683216 | Zbl 0922.14004

[16] Lopez A.F., Noether-Lefschetz Theory and the Picard Group of Projective Surfaces, Mem. Amer. Math. Soc., vol. 89, American Mathematical Society, Providence, RI, 1991. | MR 1043786 | Zbl 0736.14012

[17] Milnor J., Singular Points of Complex Hypersurfaces, Ann. of Math. Stud., vol. 61, Princeton University Press, Princeton, NJ, 1968. | MR 239612 | Zbl 0184.48405

[18] Otwinowska A., Composantes de petite codimension du lieu de Noether-Lefschetz; un argument en faveur de la conjecture de Hodge pour les hypersurfaces, J. Algebraic Geom. 12 (2003) 307-320. | MR 1949646 | Zbl 1080.14506

[19] Otwinowska A., Monodromie d'une famille d'hypersurfaces, Preprint.

[20] Otwinowska A., Sur les variétés de Hodge des hypersurfaces, math.AG/0401092.

[21] Saito M., Modules de Hodge polarisables, Publ. RIMS, Kyoto Univ. 24 (1988) 849-995. | MR 1000123 | Zbl 0691.14007

[22] Saito M., Mixed Hodge modules, Publ. RIMS, Kyoto Univ. 26 (1990) 221-333. | MR 1047415 | Zbl 0727.14004

[23] Saito M., Admissible normal functions, J. Algebra Geom. 5 (1996) 235-276. | MR 1374710 | Zbl 0918.14018

[24] Steenbrink J.H.M., Limits of Hodge structures, Invent. Math. 31 (1975/76) 229-257. | MR 429885 | Zbl 0303.14002

[25] Steenbrink J.H.M., Zucker S., Variation of mixed Hodge structure I, Invent. Math. 80 (1985) 489-542. | MR 791673 | Zbl 0626.14007

[26] Verdier J.-L., Catégories dérivées, in: SGA 4 1/2, Lecture Notes in Math., vol. 569, Springer, Berlin, 1977, pp. 262-311. | MR 463174 | Zbl 0407.18008

[27] Verdier J.-L., Dualité dans la cohomologie des espaces localement compacts, Sém. Bourbaki (1965/66), Exp. no 300 Collection hors série de la SMF 9 (1995) 337-349. | Numdam | MR 1610971 | Zbl 0268.55006

[28] Voisin C., Hodge Theory and Complex Algebraic Geometry, II, Cambridge University Press, Cambridge, 2003. | MR 1997577 | Zbl 1032.14002

[29] Zucker S., Hodge theory with degenerating coefficients, L 2 -cohomology in the Poincaré metric, Ann. of Math. 109 (1979) 415-476. | MR 534758 | Zbl 0446.14002