The hard Lefschetz theorem and the topology of semismall maps
de Cataldo, Mark Andrea A ; Migliorini, Luca
Annales scientifiques de l'École Normale Supérieure, Tome 35 (2002), p. 759-772 / Harvested from Numdam
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@article{ASENS_2002_4_35_5_759_0,
     author = {de Cataldo, Mark Andrea A. and Migliorini, Luca},
     title = {The hard Lefschetz theorem and the topology of semismall maps},
     journal = {Annales scientifiques de l'\'Ecole Normale Sup\'erieure},
     volume = {35},
     year = {2002},
     pages = {759-772},
     doi = {10.1016/s0012-9593(02)01108-4},
     mrnumber = {1951443},
     zbl = {1021.14004},
     language = {en},
     url = {http://dml.mathdoc.fr/item/ASENS_2002_4_35_5_759_0}
}

de Cataldo, Mark Andrea A; Migliorini, Luca. The hard Lefschetz theorem and the topology of semismall maps. Annales scientifiques de l'École Normale Supérieure, Tome 35 (2002) pp. 759-772. doi : 10.1016/s0012-9593(02)01108-4. http://gdmltest.u-ga.fr/item/ASENS_2002_4_35_5_759_0/

[1] Beilinson A.A., Bernstein J.N., Deligne P., Faisceaux pervers, Astérisque 100 (1982). | MR 751966 | Zbl 0536.14011

[2] Borel A. et al. , Intersection Cohomology, Progress in Mathematics, 50, Birkhäuser, Boston, 1984. | MR 788171 | 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] Chriss N., Ginzburg V., Representation Theory and Complex Geometry, Birkhäuser, Boston, 1997. | MR 1433132 | Zbl 0879.22001

[5] De Cataldo M., Migliorini L., The Douady space of a complex surface, Adv. in Math. 151 (2000) 283-312. | MR 1758249 | Zbl 0991.32006

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

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

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

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

[10] Esnault H., Viehweg E., Vanishing and non-vanishing theorems, Actes du Colloque de Théorie de Hodge, Astérisque 179-180 (1989) 97-112. | MR 1042803 | Zbl 0705.14018

[11] Fulton W., Intersection Theory, Ergebnisse der Mathematik, 3.folge. Band 2, Springer-Verlag, Berlin, 1984. | MR 732620 | Zbl 0885.14002

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

[13] Goresky M., Macpherson R., Stratified Morse Theory, Ergebnisse der Mathematik, 3.folge. Band 2, Springer-Verlag, Berlin, 1988. | MR 932724 | Zbl 0639.14012

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

[15] Laufer H., Normal Two-Dimensional Singularities, Annals of Mathematics Studies, 71, Princeton University Press, 1971. | MR 320365 | Zbl 0245.32005

[16] Looijenga E., Cohomology and intersection hohomology of algebraic varieties, in: Kollár J. (Ed.), Complex Algebraic Geometry, IAS/Park City Mathematics Series, 3, American Mathematical Society, 1997, pp. 221-264. | MR 1442524 | Zbl 0910.14006

[17] Migliorini L., A smooth family of minimal surfaces of general type over a curve of genus at most one is trivial, J. Algebraic Geometry 4 (1995) 353-361. | MR 1311355 | Zbl 0834.14021

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

[19] Wiśniewski J.A., Cohomological invariants of complex manifolds coming from extremal rays, Asian J. Math. 2 (2) (1998) 289-302. | MR 1639552 | Zbl 0949.14008