IJPAM: Volume 67, No. 1 (2011)

LINE BUNDLES ON CURVES OVER
A NON-ALGEBRAICALLY CLOSED FIELD

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


Abstract.Let $Y$ be an integral projective curve defined over a field $K$. Set $g:= p_a(Y)$. Here we give conditions on $\sharp (Y_{reg}(K))$ assuring the existence of $L\in \mbox{Pic}^{g-1}(Y)$ defined over $K$ and such that $h^0(Y,L)=h^1(Y,L)=0$.

Received: November 28, 2010

AMS Subject Classification: 14NH

Key Words and Phrases: line bundle, curve over a finite field

Source: International Journal of Pure and Applied Mathematics
ISSN: 1311-8080
Year: 2011
Volume: 67
Issue: 1