IJPAM: Volume 54, No. 3 (2009)

GENERAL DEGREE $g-1$ LINE BUNDLES
ON REDUCIBLE CURVES

E. Ballico
Department of Mathematics
University of Trento
38 123 Povo (Trento) - Via Sommarive, 14, ITALY
e-mail: [email protected]


Abstract.Let $X$ be a reduced and connected projective curve. Here we show the existence of a degree $p_a(X)-1$ line bundle $L$ on $X$ such that $h^1(X,L)=0$. If $X$ is semistable, then we may take $L$ semibalanced in the sense of Caporaso.

Received: June 1, 2009

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

Key Words and Phrases: semistable curve, balanced line bundle

Source: International Journal of Pure and Applied Mathematics
ISSN: 1311-8080
Year: 2009
Volume: 54
Issue: 3