IJPAM: Volume 52, No. 4 (2009)

BRILL-NOETHER THEORY ON SINGULAR CURVES
(EXAMPLES WITH NON-EXISTENCE)

E. Ballico
Department of Mathematics
University of Trento
380 50 Povo (Trento) - Via Sommarive, 14, ITALY
e-mail: ballico@science.unitn.it


Abstract.Here we discuss the existence of stable curves $X$ with the Brill-Nother theory of a general curve of its genus, but whose gonality is not computed by line bundles on $X$. We classify all the examples in genus $4$. We do not have new examples for genus $\ge 5$.

Received: March 23, 2009

AMS Subject Classification: 14H20, 14H51

Key Words and Phrases: gonality, stable curve

Source: International Journal of Pure and Applied Mathematics
ISSN: 1311-8080
Year: 2009
Volume: 52
Issue: 4