IJPAM: Volume 22, No. 1 (2005)

THE SUBGROUP OF THE JACOBIAN OF
A PROJECTIVE CURVE GENERATED BY
A GENERIC HYPERPLANE SECTION

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


Abstract.Let $C \subset {\bf {P}}^r$ be an integral non-degenerate curve and $f: X \to C$ its normalization. If $\mbox{\rm char}(\mathbb {K}) > 0$ assume that $C$ is reflexive. Set $d:= \mbox{\rm deg}(C)$. Let $E_C \subset \mbox{\rm Pic}^0(X)$ be the subgroup induced by the differences of the points of a generic hyperplane section of $C$. Here we prove that $E_C \cong \mathbb {Z}^{d-1}$. A similar result is proven when we only consider the hyperplane sections tangent to a general (but fixed) $P\in C$.

Received: May 5, 2005

AMS Subject Classification: 14H50, 14H40

Key Words and Phrases: projective curves, hyperplane section, Jacobian

Source: International Journal of Pure and Applied Mathematics
ISSN: 1311-8080
Year: 2005
Volume: 22
Issue: 1