# IJPAM: Volume 27, No. 2 (2006)

**STABLE COHERENT SYSTEMS ON INTEGRAL**

PROJECTIVE CURVES: AN ASYMPTOTIC

EXISTENCE THEOREM

PROJECTIVE CURVES: AN ASYMPTOTIC

EXISTENCE THEOREM

Department of Mathematics

University of Trento

380 50 Povo (Trento) - Via Sommarive, 14, ITALY

e-mail: [email protected]

**Abstract.**Fix integers , an integral projective curve , a rank vector bundle on and an ample line bundle on . Here we prove the existence of an integer (depending only on ) such that for all integers a general -dimensional linear subspace of
spans and the coherent system is -stable for every . To prove this result we prove the existence of an integer (depending only on ) such that for all integers a general -dimensional linear subspace of
spans and the natural map
is injective.

**Received: **October 21, 2005

**AMS Subject Classification: **14H60

**Key Words and Phrases: **coherent systems on curves, vector bundles on curves, stable vector bundles, integral curve

**Source:** International Journal of Pure and Applied Mathematics

**ISSN:** 1311-8080

**Year:** 2006

**Volume:** 27

**Issue:** 2