Monodromy of a family of hypersurfaces containing a given subvariety

Ania Otwinowska; Morihiko Saito

Annales scientifiques de l'École Normale Supérieure (2005)

  • Volume: 38, Issue: 3, page 365-386
  • ISSN: 0012-9593

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Otwinowska, Ania, and Saito, Morihiko. "Monodromy of a family of hypersurfaces containing a given subvariety." Annales scientifiques de l'École Normale Supérieure 38.3 (2005): 365-386. <http://eudml.org/doc/82662>.

@article{Otwinowska2005,
author = {Otwinowska, Ania, Saito, Morihiko},
journal = {Annales scientifiques de l'École Normale Supérieure},
keywords = {hypersurface; Lefschetz pencil; degeneration; nearby cycles; vanishing cohomology},
language = {eng},
number = {3},
pages = {365-386},
publisher = {Elsevier},
title = {Monodromy of a family of hypersurfaces containing a given subvariety},
url = {http://eudml.org/doc/82662},
volume = {38},
year = {2005},
}

TY - JOUR
AU - Otwinowska, Ania
AU - Saito, Morihiko
TI - Monodromy of a family of hypersurfaces containing a given subvariety
JO - Annales scientifiques de l'École Normale Supérieure
PY - 2005
PB - Elsevier
VL - 38
IS - 3
SP - 365
EP - 386
LA - eng
KW - hypersurface; Lefschetz pencil; degeneration; nearby cycles; vanishing cohomology
UR - http://eudml.org/doc/82662
ER -

References

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  1. [1] Beilinson A., Bernstein J., Deligne P., Faisceaux pervers, Astérisque, vol. 100, Soc. Math. France, Paris, 1982. Zbl0536.14011MR751966
  2. [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. Zbl0471.14003MR605338
  3. [3] Clemens H., Degeneration of Kähler manifolds, Duke Math. J.44 (1977) 215-290. Zbl0353.14005MR444662
  4. [4] Deligne P., Théorie de Hodge I, Actes Congrès Intern. Math.1 (1970) 425-430. Zbl0219.14006MR441965
  5. [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. Zbl0266.14008
  6. [6] Deligne P., La formule de Picard–Lefschetz, in: SGA7 XV, Lecture Notes in Math., vol. 340, Springer, Berlin, 1973, pp. 165-197. Zbl0266.14010
  7. [7] Dimca A., Sheaves in Topology, Universitext, Springer, Berlin, 2004. Zbl1043.14003MR2050072
  8. [8] Dimca A., Saito M., Monodromy at infinity and the weights of cohomology, Compositio Math.138 (2003) 55-71. Zbl1039.32037MR2002954
  9. [9] Eisenbud D., Commutative Algebra with a View Toward Algebraic Geometry, Springer, New York, 1995. Zbl0819.13001MR1322960
  10. [10] Griffiths P., Harris J., On the Noether–Lefschetz theorem and some remarks on codimension two cycles, Math. Ann.271 (1985) 31-51. Zbl0552.14011MR779603
  11. [11] Illusie L., Autour du théorème de monodromie locale, Astérisque223 (1994) 9-57. Zbl0837.14013MR1293970
  12. [12] Katz N., Étude cohomologique des pinceaux de Lefschetz, in: Lecture Notes in Math., vol. 340, Springer, Berlin, 1973, pp. 254-327. Zbl0284.14007
  13. [13] Kleiman S., Altman A., Bertini theorems for hypersurface sections containing a subscheme, Comm. Algebra7 (1979) 775-790. Zbl0401.14002MR529493
  14. [14] Lefschetz S., L'analysis situs et la géométrie algébrique, Gauthier-Villars, Paris, 1924. JFM50.0663.01
  15. [15] Lewis J.D., A Survey of the Hodge Conjecture, Monograph Series, vol. 10, American Mathematical Society, Providence RI, 1999. Zbl0922.14004MR1683216
  16. [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. Zbl0736.14012MR1043786
  17. [17] Milnor J., Singular Points of Complex Hypersurfaces, Ann. of Math. Stud., vol. 61, Princeton University Press, Princeton, NJ, 1968. Zbl0184.48405MR239612
  18. [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. Zbl1080.14506MR1949646
  19. [19] Otwinowska A., Monodromie d'une famille d'hypersurfaces, Preprint. 
  20. [20] Otwinowska A., Sur les variétés de Hodge des hypersurfaces, math.AG/0401092. 
  21. [21] Saito M., Modules de Hodge polarisables, Publ. RIMS, Kyoto Univ.24 (1988) 849-995. Zbl0691.14007MR1000123
  22. [22] Saito M., Mixed Hodge modules, Publ. RIMS, Kyoto Univ.26 (1990) 221-333. Zbl0727.14004MR1047415
  23. [23] Saito M., Admissible normal functions, J. Algebra Geom.5 (1996) 235-276. Zbl0918.14018MR1374710
  24. [24] Steenbrink J.H.M., Limits of Hodge structures, Invent. Math.31 (1975/76) 229-257. Zbl0303.14002MR429885
  25. [25] Steenbrink J.H.M., Zucker S., Variation of mixed Hodge structure I, Invent. Math.80 (1985) 489-542. Zbl0626.14007MR791673
  26. [26] Verdier J.-L., Catégories dérivées, in: SGA 4 1/2, Lecture Notes in Math., vol. 569, Springer, Berlin, 1977, pp. 262-311. Zbl0407.18008MR463174
  27. [27] Verdier J.-L., Dualité dans la cohomologie des espaces localement compacts, Sém. Bourbaki (1965/66), Exp. no 300 Collection hors série de la SMF9 (1995) 337–349. Zbl0268.55006MR1610971
  28. [28] Voisin C., Hodge Theory and Complex Algebraic Geometry, II, Cambridge University Press, Cambridge, 2003. Zbl1032.14002MR1997577
  29. [29] Zucker S., Hodge theory with degenerating coefficients, L 2 -cohomology in the Poincaré metric, Ann. of Math.109 (1979) 415-476. Zbl0446.14002MR534758

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