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

How to cite

top

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

top
  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

NotesEmbed ?

top

You must be logged in to post comments.

To embed these notes on your page include the following JavaScript code on your page where you want the notes to appear.

Only the controls for the widget will be shown in your chosen language. Notes will be shown in their authored language.

Tells the widget how many notes to show per page. You can cycle through additional notes using the next and previous controls.

    
                

Note: Best practice suggests putting the JavaScript code just before the closing </body> tag.