no. 5
The Hodge theory of algebraic maps
Annales scientifiques de l'École Normale Supérieure, Série 4, Tome 38 (2005) no. 5, pp. 693-750 
@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},
     pages = {693--750},
     year = {2005},
     publisher = {Elsevier},
     volume = {Ser. 4, 38},
     number = {5},
     doi = {10.1016/j.ansens.2005.07.001},
     mrnumber = {2195257},
     zbl = {1094.14005},
     language = {en},
     url = {https://www.numdam.org/articles/10.1016/j.ansens.2005.07.001/}
}
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de Cataldo, Mark Andrea A.; Migliorini, Luca. The Hodge theory of algebraic maps. Annales scientifiques de l'École Normale Supérieure, Série 4, Tome 38 (2005) no. 5, pp. 693-750. doi: 10.1016/j.ansens.2005.07.001

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

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

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

[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. | Zbl | MR

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

[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. | Zbl | MR | Numdam

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

[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. | Zbl | MR | Numdam

[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. | Zbl | MR

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

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

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

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

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

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

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

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

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

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

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

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

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

[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

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

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

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

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

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

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

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

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