Let be a projective algebraic manifold, and be the sheaf of nonvanishing meromorphic functions on X in the analytic topology. We prove a number of nonvanishing results for . In particular, is acyclic iff .
Sur une variété algébrique projective lisse , soit le faisceau des germes de fonctions méromorphes non nulles pour la topologie analytique de X. Nous démontrons un certain nombre de résultats de non annulation pour la cohomologie . En particulier, le faisceau est acyclique si et seulement si X est de dimension 1.
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Xi Chen 1; Matt Kerr 2; James D. Lewis 1
@article{CRMATH_2010__348_5-6_291_0, author = {Xi Chen and Matt Kerr and James D. Lewis}, title = {The sheaf of nonvanishing meromorphic functions in the projective algebraic case is not acyclic}, journal = {Comptes Rendus. Math\'ematique}, pages = {291--293}, publisher = {Elsevier}, volume = {348}, number = {5-6}, year = {2010}, doi = {10.1016/j.crma.2010.02.008}, language = {en}, }
TY - JOUR AU - Xi Chen AU - Matt Kerr AU - James D. Lewis TI - The sheaf of nonvanishing meromorphic functions in the projective algebraic case is not acyclic JO - Comptes Rendus. Mathématique PY - 2010 SP - 291 EP - 293 VL - 348 IS - 5-6 PB - Elsevier DO - 10.1016/j.crma.2010.02.008 LA - en ID - CRMATH_2010__348_5-6_291_0 ER -
%0 Journal Article %A Xi Chen %A Matt Kerr %A James D. Lewis %T The sheaf of nonvanishing meromorphic functions in the projective algebraic case is not acyclic %J Comptes Rendus. Mathématique %D 2010 %P 291-293 %V 348 %N 5-6 %I Elsevier %R 10.1016/j.crma.2010.02.008 %G en %F CRMATH_2010__348_5-6_291_0
Xi Chen; Matt Kerr; James D. Lewis. The sheaf of nonvanishing meromorphic functions in the projective algebraic case is not acyclic. Comptes Rendus. Mathématique, Volume 348 (2010) no. 5-6, pp. 291-293. doi : 10.1016/j.crma.2010.02.008. https://comptes-rendus.academie-sciences.fr/mathematique/articles/10.1016/j.crma.2010.02.008/
[1] Classification and embeddings of surfaces, Proceedings of Symposia in Pure Mathematics, Volume 29 (1975), pp. 329-420
[2] Panorama des Mathématiques Pures, Gauthier–Villars, 1977
[3] A Survey of the Hodge Conjecture, CRM Monograph Series, vol. 10, AMS, Providence, 1999
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