IJPAM: Volume 52, No. 2 (2009)

ON THE FAILURE OF CLIFFORD'S INEQUALITY
FOR LINE BUNDLES ON REDUCIBLE CURVES

E. Ballico
Department of Mathematics
University of Trento
380 50 Povo (Trento) - Via Sommarive, 14, ITALY
e-mail: [email protected]


Abstract.We give a cheap way to construct pairs $(X,L)$ with $X$ a stable curve and $L\in \mbox{Pic}(X)$ such that $L$ is ample and spanned, $\deg (L) \le 2p_a(X)-2$ and $h^0(X,L) > \deg (L)/2+1$, i.e. $L$ does not satisfy Clifford's inequality.

Received: March 12, 2009

AMS Subject Classification: 14H51, 14H10, 14H20

Key Words and Phrases: reducible curve, Clifford's inequality, stable curve

Source: International Journal of Pure and Applied Mathematics
ISSN: 1311-8080
Year: 2009
Volume: 52
Issue: 2