IJPAM: Volume 12, No. 4 (2004)

ON THE INJECTIVITY OF THE SYMMETRIC
MULTIPLICATION MAP FOR LINE BUNDLES
ON SMOOTH PROJECTIVE CURVES, II

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 a smooth projective curve and $L\in \mbox{\rm Pic}(X)$. Here we study the injectivity the symmetric multiplication map $\mu _L: S^2(H^0(X,L)) \to H^0(X,L^{\otimes 2})$ for certain double coverings of high genus curves.

Received: February 3, 2004

AMS Subject Classification: 14H50, 14H51

Key Words and Phrases: symmetric multiplication map, line bundle, line bundles on curves, double covering of curves

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