IJPAM: Volume 69, No. 1 (2011)

SINGULAR CURVES WITH LINE BUNDLES $L$
DEFINED OVER $\mathbb {F}_q$ AND WITH GOOD COHOMOLOGY

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


Abstract. Here (following a previous paper of mine) we prove the existence of several pairs $(X,L)$, where $X$ is a geometrically integral projective curve defined over $\mathbb {F}_q$ and $L$ is a line bundle on $X$ defined over $\mathbb {F}_q$ and with either $H^0(X,L)=0$ or $H^1(X,L)=0$. These examples are obtained using the existence of similar line bundles on the normalization of $X$, i.e. a case studied by C. Ballet, C. Ritzenthaler and R. Roland.

Received: January 18, 2011

AMS Subject Classification: 14H20, 14H05, 12E20

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

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Source: International Journal of Pure and Applied Mathematics
ISSN printed version: 1311-8080
ISSN on-line version: 1314-3395
Year: 2011
Volume: 69
Issue: 1