Théorèmes de Lefschetz pour les lieux de dégénérescence
Debarre, Olivier
Bulletin de la Société Mathématique de France, Tome 128 (2000), p. 283-308 / Harvested from Numdam
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@article{BSMF_2000__128_2_283_0,
     author = {Debarre, Olivier},
     title = {Th\'eor\`emes de Lefschetz pour les lieux de d\'eg\'en\'erescence},
     journal = {Bulletin de la Soci\'et\'e Math\'ematique de France},
     volume = {128},
     year = {2000},
     pages = {283-308},
     doi = {10.24033/bsmf.2371},
     mrnumber = {2002b:14051},
     zbl = {0964.14016},
     language = {fr},
     url = {http://dml.mathdoc.fr/item/BSMF_2000__128_2_283_0}
}

Debarre, Olivier. Théorèmes de Lefschetz pour les lieux de dégénérescence. Bulletin de la Société Mathématique de France, Tome 128 (2000) pp. 283-308. doi : 10.24033/bsmf.2371. http://gdmltest.u-ga.fr/item/BSMF_2000__128_2_283_0/

[ACGH] Arbarello (E.), Cornalba (M.), Griffiths (P.), Harris (J.). - Geometry of algebraic curves, I. - Grundlehren 267, Springer-Verlag, New York, 1985. | MR 86h:14019 | Zbl 0559.14017

[B] Bertram (A.). - An existence theorem for Prym special divisors, Invent. Math., t. 90, 1987, p. 669-671. | MR 88k:14016 | Zbl 0646.14006

[De] Deligne (P.). - Théorie de Hodge, III, Publ. Math. I.H.E.S., t. 44, 1974, p. 5-77. | Numdam | MR 58 #16653b | Zbl 0237.14003

[dB] Du Bois (Ph.). - Complexe de de Rham filtré d'une variété singulière, Bull. Soc. Math. France, t. 109, 1981, p. 41-81. | Numdam | MR 82j:14006 | Zbl 0465.14009

[EG] Edidin (D.), Graham (W.). - Characteristic Classes and Quadric Bundles, Duke Math. J., t. 78, 1995, p. 277-299. | MR 98a:14004 | Zbl 0932.14003

[E] Ein (L.). - An Analogue of Max Noether's Theorem, Duke Math. J., t. 52, 1985, p. 689-706. | MR 87e:14029 | Zbl 0589.14034

[EP] Ellingsrud (G.), Peskine (C.). - Équivalence numérique pour les surfaces génériques d'une famille lisse de surfaces projectives, in Problems in the theory of surfaces and their classification (Cortona, 1988), p. 99-109, Sympos. Math., XXXII. - Academic Press, London, 1991. | Zbl 0838.14004

[F1] Fulton (W.). - Intersection theory. - Ergebnisse der Mathematik und ihrer Grenzgebiete 2, Springer Verlag, Berlin, 1984. | MR 85k:14004 | Zbl 0541.14005

[F2] Fulton (W.). - Schubert varieties in flag bundles for the classical groups, in Proceedings of the Hirzebruch 65 Conference on Algebraic Geometry (Ramat Gan, 1993), p. 241-262. - Israel Math. Conf. Proc., 9, Bar-Ilan Univ., Ramat Gan, 1996. | Zbl 0862.14032

[FL] Fulton (W.), Lazarsfeld (R.). - On the connectedness of degeneracy loci and special divisors, Acta Math., t. 146, 1981, p. 271-283. | MR 82k:14016 | Zbl 0469.14018

[G1] Grothendieck (A.). - Techniques de descente et théorèmes d'existence en géométrie algébrique, VI. Les schémas de Picard : propriétés générales, Séminaire Bourbaki, exp. 236, 1961/1962. | Numdam | Zbl 0238.14015

[G2] Grothendieck (A.). - Cohomologie locale des faisceaux cohérents et théorèmes de Lefschetz locaux et globaux (SGA2). - Masson et North Holland, Paris Amsterdam, 1968. | MR 57 #16294 | Zbl 0197.47202

[H1] Hamm (H.). - Lefschetz theorems for singular varieties, in Singularities, Part 1 (Arcata, Calif., 1981), p. 547-557. - Proc. Sympos. Pure Math., 40, Amer. Math. Soc., Providence, R.I., 1983. | Zbl 0525.14011

[H2] Hamm (H.). - Zur Homotopietyp Steinscher Räume, J. reine angew. Math., t. 338, 1983, p. 121-135. | MR 84i:32021 | Zbl 0491.32010

[Ha] Harris (J.). - Theta-characteristics on algebraic curves, Trans. Amer. Math. Soc., t. 271, 1982, p. 611-638. | MR 83m:14022 | Zbl 0513.14025

[K] Kollár (J.). - Shafarevich maps and automorphic forms. - M.B. Porter Lectures, Princeton University Press, Princeton, NJ, 1995. | MR 96i:14016 | Zbl 0871.14015

[L] Laytimi (F.). - On Degeneracy Loci, Int. J. Math., t. 7, 1996, p. 745-754. | MR 98a:14064 | Zbl 0910.14003

[Lo] López (A.). - Noether-Lefschetz theory and the Picard group of projective surfaces, Mem. Amer. Math. Soc., t. 89, 1991. | MR 91f:14030 | Zbl 0736.14012

[M] Macdonald (I.). - Symmetric Products of an Algebraic Curve, Topology, t. 1, 1962, p. 319-343. | MR 27 #1445 | Zbl 0121.38003

[Ma] Manivel (L.). - Vanishing theorems for ample vector bundles, Invent. Math., t. 127, 1997, p. 401-416. | MR 98e:14016 | Zbl 0906.14011

[Mu] Mumford (D.). - Theta characteristics of an algebraic curve, Ann. Sci. École Norm. Sup., t. 4, 1971, p. 181-192. | Numdam | MR 45 #1918 | Zbl 0216.05904

[P1] Pragacz (P.). - Cycles of isotropic subspaces and formulas for symmetric degeneracy loci, Banach Center Publications, t. 26 (2), 1990, p. 189-199. | MR 93h:14036 | Zbl 0743.14009

[P2] Pragacz (P.). - Algebro-geometric applications of Schur S - and Q-polynomials, in Topics in invariant theory (Paris, 1989/1990), Lecture Notes in Math., t. 1478, Springer, Berlin, 1991, p. 130-191. | MR 93h:05170 | Zbl 0783.14031

[PR1] Pragacz (P.), Ratajski (J.). - A Pieri-type theorem for Lagrangian and odd Orthogonal Grassmannians, J. reine angew. Math., t. 476, 1996, p. 143-189. | MR 97i:14032 | Zbl 0847.14029

[PR2] Pragacz (P.), Ratajski (J.). - Formulas for Lagrangian and orthogonal degeneracy loci ; Q-polynomial approach, Comp. Math., t. 107, 1997, p. 11-87. | MR 98g:14063 | Zbl 0916.14026

[RX] Rosselló Lompart (F.), Xambó Descamps (S.). - Computing Chow Groups, in Algebraic Geometry (Sundance, UT, 1986), A. Holme, R. Speiser ed., Lecture Notes in Math., t. 1311, Springer, Berlin-New York, 1988, p. 220-234. | Zbl 0663.14001

[S] Spandaw (J.). - Noether-Lefschetz Theorems for Degeneracy Loci. - Habilitationsschrift, Hannover, 2000.

[St] Steffen (F.). - Eine Verallgemeinerung des Krullschen Hauptidealsatzes mit einer Anwendung auf die Brill-Noether-Theorie. - Dissertation, Bochum, 1996.

[T] Tu (L.). - The Connectedness of Symmetric and Skew-Symmetric Degeneracy Loci : Even Ranks, Trans. Amer. Math. Soc., t. 313, 1989, p. 381-392. | MR 89i:14043 | Zbl 0689.14024

[W] Welters (G.). - A theorem of Gieseker-Petri type for Prym varieties, Ann. Sci. École Norm. Sup., t. 18, 1985, p. 671-683. | Numdam | MR 88a:14034 | Zbl 0628.14036