The Hodge theory of algebraic maps

Mark Andrea A. de Cataldo; Luca Migliorini

Annales scientifiques de l'École Normale Supérieure (2005)

  • Volume: 38, Issue: 5, page 693-750
  • ISSN: 0012-9593

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de Cataldo, Mark Andrea A., and Migliorini, Luca. "The Hodge theory of algebraic maps." Annales scientifiques de l'École Normale Supérieure 38.5 (2005): 693-750. <http://eudml.org/doc/82672>.

@article{deCataldo2005,
author = {de Cataldo, Mark Andrea A., Migliorini, Luca},
journal = {Annales scientifiques de l'École Normale Supérieure},
keywords = {intersection cohomology; perverse sheaves},
language = {eng},
number = {5},
pages = {693-750},
publisher = {Elsevier},
title = {The Hodge theory of algebraic maps},
url = {http://eudml.org/doc/82672},
volume = {38},
year = {2005},
}

TY - JOUR
AU - de Cataldo, Mark Andrea A.
AU - Migliorini, Luca
TI - The Hodge theory of algebraic maps
JO - Annales scientifiques de l'École Normale Supérieure
PY - 2005
PB - Elsevier
VL - 38
IS - 5
SP - 693
EP - 750
LA - eng
KW - intersection cohomology; perverse sheaves
UR - http://eudml.org/doc/82672
ER -

References

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  1. [1] Beilinson A.A., Bernstein J.N., Deligne P., Faisceaux pervers, Astérisque, vol. 100, Soc. Math. France, Paris, 1982. Zbl0536.14011MR751966
  2. [2] Borel A. et al. , Intersection Cohomology, Progr. Math., vol. 50, Birkhäuser, Boston, 1984. Zbl0553.14002
  3. [3] Borho W., MacPherson R., Partial resolutions of nilpotent varieties, Astérisque101–102 (1983) 23-74. Zbl0576.14046MR737927
  4. [4] Cattani E., Kaplan A., Schmid W., L 2 and intersection cohomologies for a polarizable variation of Hodge structure, Invent. Math.87 (1987) 217-252. Zbl0611.14006MR870728
  5. [5] Clemens C.H., Degeneration of Kähler manifolds, Duke Math. J.44 (2) (1977) 215-290. Zbl0353.14005MR444662
  6. [6] de Cataldo M., Migliorini L., The Hard Lefschetz theorem and the topology of semismall maps, Ann. Sci. École Norm. Sup. (4)35 (5) (2002) 759-772. Zbl1021.14004MR1951443
  7. [7] de Cataldo M., Migliorini L., The Chow Motive of semismall resolutions, Math. Res. Lett.11 (2004) 151-170. Zbl1073.14010MR2067464
  8. [8] de Cataldo M., Migliorini L., The Hodge theory of algebraic maps, math.AG/0306030. Zbl1094.14005
  9. [9] Deligne P., Théorème de Lefschetz et critères de dégénérescence de suites spectrales, Publ. Math. IHÉS35 (1969) 107-126. Zbl0159.22501MR244265
  10. [10] Deligne P., Décompositions dans la catégorie dérivée, in: Motives, Seattle, WA, 1991, Part 1, Proc. Sympos. Pure Math., vol. 55, American Mathematical Society, Providence, RI, 1994, pp. 115-128. Zbl0809.18008MR1265526
  11. [11] Deligne P., Théorie de Hodge, II, Publ. Math. IHÉS40 (1971) 5-57. Zbl0219.14007MR498551
  12. [12] Deligne P., Théorie de Hodge, III, Publ. Math. IHÉS44 (1974) 5-78. Zbl0237.14003MR498552
  13. [13] Deligne P., La conjecture de Weil, II, Publ. Math. IHÉS52 (1980) 138-252. Zbl0456.14014MR601520
  14. [14] Dimca A., Sheaves in Topology, Universitext, Springer, Berlin, 2004. Zbl1043.14003MR2050072
  15. [15] El Zein F., Théorie de Hodge des cycles évanescents, Ann. Sci. École Norm. Sup. (4)19 (1986) 107-184. Zbl0538.14003MR860812
  16. [16] Goresky M., MacPherson R., Intersection homology II, Invent. Math.71 (1983) 77-129. Zbl0529.55007MR696691
  17. [17] Goresky M., MacPherson R., Stratified Morse Theory, Ergeb. Math. (3), vol. 2, Springer, Berlin, 1988. Zbl0639.14012MR932724
  18. [18] Guillen F., Navarro Aznar V., Sur le théorème local des cycles invariants, Duke Math. J.61 (1) (1990) 133-155. Zbl0722.14002MR1068383
  19. [19] Iversen B., Cohomology of Sheaves, Universitext, Springer, Berlin, 1986. Zbl1272.55001MR842190
  20. [20] Kashiwara M., Kawai T., The Poincaré lemma for variations of polarized Hodge structures, Publ. Res. Inst. Math. Sci.23 (1987) 345-407. Zbl0629.14005MR890924
  21. [21] Kashiwara M., Schapira P., Sheaves on Manifolds, Grundlehren Math. Wiss., vol. 292, Springer, Berlin, 1990. Zbl0709.18001MR1074006
  22. [22] R. MacPherson, Global questions in the topology of singular spaces, in: Proc. of the ICM, 1983, Warszawa, pp. 213–235. Zbl0612.57012MR804683
  23. [23] Mochizuki T., Asymptotic behaviour of tame nilpotent harmonic bundles with trivial parabolic structure, J. Differential Geom.62 (2002) 351-559. Zbl1069.32010MR2005295
  24. [24] Mochizuki T., Asymptotic behaviour of tame harmonic bundles and an application to pure twistor D-modules, math.DG/0312230. 
  25. [25] C. Sabbah, Polarizable twistor D-modules, Preprint. MR2156523
  26. [26] Saito M., Modules de Hodge polarisables, Publ. Res. Inst. Math. Sci.24 (6) (1988) 849-995. Zbl0691.14007MR1000123
  27. [27] Saito M., Mixed Hodge modules, Publ. Res. Inst. Math. Sci.26 (2) (1990) 221-333. Zbl0727.14004MR1047415
  28. [28] Saito M., Decomposition theorem for proper Kähler morphisms, Tohoku Math. J. (2)42 (2) (1990) 127-147. Zbl0699.14009MR1053945
  29. [29] Sommese A.J., Submanifolds of Abelian varieties, Math. Ann.233 (3) (1978) 229-256. Zbl0381.14007MR466647
  30. [30] Steenbrink J., Limits of Hodge structures, Invent. Math.31 (1975–1976) 229-257. Zbl0303.14002MR429885
  31. [31] Steenbrink J., Zucker S., Variation of mixed Hodge structure. I, Invent. Math.80 (3) (1985) 489-542. Zbl0626.14007MR791673
  32. [32] Voisin C., Théorie de Hodge et géométrie algébrique complexe, Cours spécialisés, vol. 10, Société Mathématique de France, Paris, 2002. Zbl1032.14001MR1988456

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