The sheaf of nonvanishing meromorphic functions in the projective algebraic case is not acyclic

Xi Chen; Matt Kerr; James D. Lewis

doi:10.1016/j.crma.2010.02.008

The sheaf of nonvanishing meromorphic functions in the projective algebraic case is not acyclic

Xi Chen, Matt Kerr, James D. Lewis

Department of Mathematics & Statistics

Research output: Contribution to journal › Article › peer-review

2 Scopus citations

Abstract

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

Original language	English
Pages (from-to)	291-293
Number of pages	3
Journal	Comptes Rendus Mathematique
Volume	348
Issue number	5-6
DOIs	https://doi.org/10.1016/j.crma.2010.02.008
State	Published - Mar 2010

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title = "The sheaf of nonvanishing meromorphic functions in the projective algebraic case is not acyclic",

abstract = "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 dim X = 1.",

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AU - Kerr, Matt

AU - Lewis, James D.

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AB - 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 dim X = 1.

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JO - Comptes Rendus Mathematique

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IS - 5-6

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The sheaf of nonvanishing meromorphic functions in the projective algebraic case is not acyclic

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