IJPAM: Volume 12, No. 4 (2004)

RANK ONE TORSION FREE SHEAVES
ON CURVES: THE INJECTIVITY OF
THE SYMMETRIC MULTIPLICATION MAP

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


Abstract.Let $X$ be an integral projective curve and $A$ a rank one torsion free sheaf on $X$. Here we use a theorem of Teixidor to obtain for certain nodal or cuspidal $X$ the injectivity of the map $\mu _A: S^2(H^0(X,A)) \to H^0(X,S^2(A)/\mbox{Tors}(S^2(A)))$ induced from the symmetrized multiplication map for all $A$ with low degree.

Received: February 3, 2004

AMS Subject Classification: 14H20, 14H99, 14HF03

Key Words and Phrases: symmetric multiplication map, rank one torsion free sheaf, torsion free sheaf, integral curve, nodal curve

Source: International Journal of Pure and Applied Mathematics
ISSN: 1311-8080
Year: 2004
Volume: 12
Issue: 4