IJPAM: Volume 52, No. 3 (2009)

ON THE GONALITY OF NODAL REDUCIBLE PLANE
CURVES WITH SMOOTH IRREDUCIBLE COMPONENTS

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


Abstract.Let $X \subset \mathbb {P}^2$ be a nodal curve of degree $d \ge 4$ whose irreducible components are smooth. Here we prove that $X$ has ``gonality'' $d-1$ and classify all generically spanned coherent sheaves $F$ on $X$ with depth $1$, pure rank $1$, $\deg (F)=d-1$ and $h^0(X,F) \ge 2$.

Received: March 10, 2009

AMS Subject Classification: 14H20, 14H51

Key Words and Phrases: reducible plane curve, stable plane curve, gonality

Source: International Journal of Pure and Applied Mathematics
ISSN: 1311-8080
Year: 2009
Volume: 52
Issue: 3