Espaces fibrés linéaires faiblement négatifs sur un espace complexe
HTML articles powered by AMS MathViewer
- by Vincenzo Ancona PDF
- Trans. Amer. Math. Soc. 215 (1976), 45-61 Request permission
Abstract:
Let F be a coherent sheaf over a compact reduced complex space $X,L(\text {F})$ the linear fibre space associated with F, ${S^k}(\text {F})$ the kth symmetric power of F. We show that if the zero-section of $L(\text {F})$ is exceptional, then ${H^r}(X,\text {E}{ \otimes _{{O_X}}}{S^k}(\text {F})) = 0$ for every coherent sheaf E on X and for $r \geqslant 1$ and sufficiently large k. Using this result, we deduce moreover that Supp F is a Moišezon space.References
- Vincenzo Ancona, Fasci debolmente positivi su di uno spazio complesso, Atti Accad. Naz. Lincei Rend. Cl. Sci. Fis. Mat. Nat. (8) 54 (1973), 567–569 (1974) (Italian, with English summary). MR 508173
- Aldo Andreotti and Hans Grauert, Théorème de finitude pour la cohomologie des espaces complexes, Bull. Soc. Math. France 90 (1962), 193–259 (French). MR 150342, DOI 10.24033/bsmf.1581
- A. Andreotti and G. Tomassini, A remark on the vanishing of certain cohomology groups, Compositio Math. 21 (1969), 417–430. MR 261031 Séminaire Henri Cartan 13ième année: 1960/61, Familles d’espaces complexes et fondements de la géométrie analytique, fasc. 1,2, École Normale Supérieure, Secrétariat mathématique, Paris, 1962. MR 26 #3562.
- Gerd Fischer, Lineare Faserräume und kohärente Modulgarben über komplexen Räumen, Arch. Math. (Basel) 18 (1967), 609–617 (German). MR 220972, DOI 10.1007/BF01898870
- Hans Grauert, Über Modifikationen und exzeptionelle analytische Mengen, Math. Ann. 146 (1962), 331–368 (German). MR 137127, DOI 10.1007/BF01441136
- Knut Knorr and Michael Schneider, Relativexzeptionelle analytische Mengen, Math. Ann. 193 (1971), 238–254 (German). MR 293129, DOI 10.1007/BF02052395
- K. Kodaira, On Kähler varieties of restricted type (an intrinsic characterization of algebraic varieties), Ann. of Math. (2) 60 (1954), 28–48. MR 68871, DOI 10.2307/1969701
- Reinhold Remmert, Holomorphe und meromorphe Abbildungen komplexer Räume, Math. Ann. 133 (1957), 328–370 (German). MR 92996, DOI 10.1007/BF01342886
- Oswald Riemenschneider, Characterizing Moišezon spaces by almost positive coherent analytic sheaves, Math. Z. 123 (1971), 263–284. MR 294714, DOI 10.1007/BF01114795
- Oswald Riemenschneider, A generalization of Kodaira’s embedding theorem, Math. Ann. 200 (1973), 99–102. MR 326009, DOI 10.1007/BF01578295
- Hugo Rossi, Picard variety of an isolated singular point, Rice Univ. Stud. 54 (1968), no. 4, 63–73. MR 244517
Additional Information
- © Copyright 1976 American Mathematical Society
- Journal: Trans. Amer. Math. Soc. 215 (1976), 45-61
- MSC: Primary 32L10
- DOI: https://doi.org/10.1090/S0002-9947-1976-0430332-3
- MathSciNet review: 0430332