IJPAM: Volume 54, No. 3 (2009)

GOOD COMPONENTS OF THE BRILL-NOETHER
SCHEME FOR GENERAL STABLE CURVES
WITH FIXED TOPOLOGICAL TYPE

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


Abstract.Let $\tau$ be a topological type for nodal projective curves and $\mathcal {M}[\tau ]$ the variety of all nodal curves with $\tau$ as topological type. Here we prove that for many $\tau$ and many multidegrees a general $X\in \mathcal {M}[\tau ]$ has a a generically smooth component with the expected dimension of the Brill-Noether scheme of morphisms $X \to \mathbb {P}^n$, $n \ge 3$, with the prescribed multidegree.

Received: June 18, 2009

AMS Subject Classification: 14H10, 14H50, 14H51

Key Words and Phrases: stable curve, Brill-Noether theory, restricted tangent bundle, multidegree

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