Comptes Rendus
Algebraic Geometry/Analytic Geometry
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.

Let X/C be a projective algebraic manifold, and MX be the sheaf of nonvanishing meromorphic functions on X in the analytic topology. We prove a number of nonvanishing results for H(X,MX). In particular, MX is acyclic iff dimX=1.

Sur une variété algébrique projective lisse X/C, soit MX 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 H(X,MX). En particulier, le faisceau MX est acyclique si et seulement si X est de dimension 1.

Received:
Accepted:
Published online:
DOI: 10.1016/j.crma.2010.02.008

Xi Chen 1; Matt Kerr 2; James D. Lewis 1

1 632 Central Academic Building, University of Alberta, Edmonton, Alberta T6G 2G1, Canada
2 104 Math. Sciences Bldg., Durham University, Durham, DH1 3LE, UK
@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] E. Bombieri; D. Husemöller Classification and embeddings of surfaces, Proceedings of Symposia in Pure Mathematics, Volume 29 (1975), pp. 329-420

[2] J. Dieudonné Panorama des Mathématiques Pures, Gauthier–Villars, 1977

[3] J.D. Lewis A Survey of the Hodge Conjecture, CRM Monograph Series, vol. 10, AMS, Providence, 1999

Cited by Sources:

Comments - Policy