IJPAM: Volume 16, No. 1 (2004)

ALGEBRAICITY CRITERIA FOR COHERENT
ANALYTIC SHEAVES ON ONE-DIMENSIONAL
STEIN SPACES

E. Ballico
Department of Mathematics
University of Trento
380 50 Povo (Trento) - Via Sommarive, 14, ITALY
e-mail: ballico@science.unitn.it


Abstract.Here we prove some algebraicity criteria for coherent analytic sheaves on one-dimensional reduced Stein spaces, e.g. the following result. Let $X$ be a one-dimensional reduced algebraic scheme and $U$ an open subset of $X_{an}$ (for the Euclidean topology). Let $G$ a coherent and torsion free analytic sheaf on $U$ which is locally free except at finitely many points of $U$. Then there is a coherent algebraic sheaf $F$ on $X$ such that $G \cong F_{an}\vert U$.

Received: July 7, 2004

AMS Subject Classification: 32L10, 30F99, 32E10

Key Words and Phrases: coherent analytic sheaf, coherent algebraic sheaf

Source: International Journal of Pure and Applied Mathematics
ISSN: 1311-8080
Year: 2004
Volume: 16
Issue: 1