The Hodge theory of algebraic maps
de Cataldo, Mark Andrea A. ; Migliorini, Luca
Annales scientifiques de l'École Normale Supérieure, Tome 38 (2005), p. 693-750 / Harvested from Numdam
Access to full text
Full (PDF)
Full (DJVU) 
@article{ASENS_2005_4_38_5_693_0,
     author = {de Cataldo, Mark Andrea A. and Migliorini, Luca},
     title = {The Hodge theory of algebraic maps},
     journal = {Annales scientifiques de l'\'Ecole Normale Sup\'erieure},
     volume = {38},
     year = {2005},
     pages = {693-750},
     doi = {10.1016/j.ansens.2005.07.001},
     mrnumber = {2195257},
     zbl = {1094.14005},
     language = {en},
     url = {http://dml.mathdoc.fr/item/ASENS_2005_4_38_5_693_0}
}

de Cataldo, Mark Andrea A.; Migliorini, Luca. The Hodge theory of algebraic maps. Annales scientifiques de l'École Normale Supérieure, Tome 38 (2005) pp. 693-750. doi : 10.1016/j.ansens.2005.07.001. http://gdmltest.u-ga.fr/item/ASENS_2005_4_38_5_693_0/

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

[2] Borel A. et al. , Intersection Cohomology, Progr. Math., vol. 50, Birkhäuser, Boston, 1984. | Zbl 0553.14002

[3] Borho W., Macpherson R., Partial resolutions of nilpotent varieties, Astérisque 101-102 (1983) 23-74. | MR 737927 | Zbl 0576.14046

[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. | MR 870728 | Zbl 0611.14006

[5] Clemens C.H., Degeneration of Kähler manifolds, Duke Math. J. 44 (2) (1977) 215-290. | MR 444662 | Zbl 0353.14005

[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. | Numdam | MR 1951443 | Zbl 1021.14004

[7] De Cataldo M., Migliorini L., The Chow Motive of semismall resolutions, Math. Res. Lett. 11 (2004) 151-170. | MR 2067464 | Zbl 1073.14010

[8] De Cataldo M., Migliorini L., The Hodge theory of algebraic maps, math.AG/0306030.

[9] Deligne P., Théorème de Lefschetz et critères de dégénérescence de suites spectrales, Publ. Math. IHÉS 35 (1969) 107-126. | Numdam | MR 244265 | Zbl 0159.22501

[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. | MR 1265526 | Zbl 0809.18008

[11] Deligne P., Théorie de Hodge, II, Publ. Math. IHÉS 40 (1971) 5-57. | Numdam | MR 498551 | Zbl 0219.14007

[12] Deligne P., Théorie de Hodge, III, Publ. Math. IHÉS 44 (1974) 5-78. | Numdam | MR 498552 | Zbl 0237.14003

[13] Deligne P., La conjecture de Weil, II, Publ. Math. IHÉS 52 (1980) 138-252. | Numdam | MR 601520 | Zbl 0456.14014

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

[15] El Zein F., Théorie de Hodge des cycles évanescents, Ann. Sci. École Norm. Sup. (4) 19 (1986) 107-184. | Numdam | MR 860812 | Zbl 0538.14003

[16] Goresky M., Macpherson R., Intersection homology II, Invent. Math. 71 (1983) 77-129. | MR 696691 | Zbl 0529.55007

[17] Goresky M., Macpherson R., Stratified Morse Theory, Ergeb. Math. (3), vol. 2, Springer, Berlin, 1988. | MR 932724 | Zbl 0639.14012

[18] Guillen F., Navarro Aznar V., Sur le théorème local des cycles invariants, Duke Math. J. 61 (1) (1990) 133-155. | MR 1068383 | Zbl 0722.14002

[19] Iversen B., Cohomology of Sheaves, Universitext, Springer, Berlin, 1986. | MR 842190

[20] Kashiwara M., Kawai T., The Poincaré lemma for variations of polarized Hodge structures, Publ. Res. Inst. Math. Sci. 23 (1987) 345-407. | MR 890924 | Zbl 0629.14005

[21] Kashiwara M., Schapira P., Sheaves on Manifolds, Grundlehren Math. Wiss., vol. 292, Springer, Berlin, 1990. | MR 1074006 | Zbl 0709.18001

[22] R. MacPherson, Global questions in the topology of singular spaces, in: Proc. of the ICM, 1983, Warszawa, pp. 213-235. | MR 804683 | Zbl 0612.57012

[23] Mochizuki T., Asymptotic behaviour of tame nilpotent harmonic bundles with trivial parabolic structure, J. Differential Geom. 62 (2002) 351-559. | MR 2005295 | Zbl 1069.32010

[24] Mochizuki T., Asymptotic behaviour of tame harmonic bundles and an application to pure twistor D-modules, math.DG/0312230.

[25] C. Sabbah, Polarizable twistor D-modules, Preprint. | MR 2156523

[26] Saito M., Modules de Hodge polarisables, Publ. Res. Inst. Math. Sci. 24 (6) (1988) 849-995. | MR 1000123 | Zbl 0691.14007

[27] Saito M., Mixed Hodge modules, Publ. Res. Inst. Math. Sci. 26 (2) (1990) 221-333. | MR 1047415 | Zbl 0727.14004

[28] Saito M., Decomposition theorem for proper Kähler morphisms, Tohoku Math. J. (2) 42 (2) (1990) 127-147. | MR 1053945 | Zbl 0699.14009

[29] Sommese A.J., Submanifolds of Abelian varieties, Math. Ann. 233 (3) (1978) 229-256. | MR 466647 | Zbl 0381.14007

[30] Steenbrink J., Limits of Hodge structures, Invent. Math. 31 (1975-1976) 229-257. | MR 429885 | Zbl 0303.14002

[31] Steenbrink J., Zucker S., Variation of mixed Hodge structure. I, Invent. Math. 80 (3) (1985) 489-542. | MR 791673 | Zbl 0626.14007

[32] Voisin C., Théorie de Hodge et géométrie algébrique complexe, Cours spécialisés, vol. 10, Société Mathématique de France, Paris, 2002. | MR 1988456 | Zbl 1032.14001