IJPAM: Volume 36, No. 3 (2007)

THE EVALUATION MAP FOR TORSION FREE
SHEAVES ON A PROJECTIVE CURVE
WITH ARITHMETIC GENUS ONE

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


Abstract.Let $C$ be an integral projective curve such that $p_a(C)=1$, $F$ a polystable vector bundle on $C$ and $F$ a torsion free sheaf on $C$. Here we study the general map $E \to F$ (injectivity or generic surjectivity or surjectivity) and the corresponding properties for the evaluation map $F\otimes H^0(C,\mbox{\rm Hom}(F,E)) \to E$.

Received: February 5, 2007

AMS Subject Classification: 14H60

Key Words and Phrases: arithmetic genus one, vector bundle, vector bundle on a cubic curve, polystable vector bundle, torsion free sheaf, evaluation map

Source: International Journal of Pure and Applied Mathematics
ISSN: 1311-8080
Year: 2007
Volume: 36
Issue: 3