Sobre gonalidade, modelos canônicos e scrolls

Abstract

Let C be an integral and projective curve; and let C' be its canonical model. We study the relation between the gonality of C and the dimension of a rational normal scroll S where C' can lie on. We are mainly interested in the case where C is singular, or even non-Gorenstein, in which case (...). We first analyze some properties of an inclusion (...) when it is induced by a pencil on C. Afterwards, in an opposite direction, weassume C' lies on a certain scroll, and check some properties C may satisfy, such as gonality and the kind of its singularities. At the end, we prove that a rational monomial curve C has gonality d if and only if C' lies on a (d -1)-fold scroll.