Combinatorial aspects of nodal curves
Abstract
To any nodal curve is associated the degree class group, a combinatorial invariant which plays an important role in the compactification of the generalised Jacobian of and in the construction of the N\'eron model of the Picard variety of families of curves having as special fibre. In this paper we study this invariant. More precisely, we construct a wide family of graphs having cyclic degree class group and we provide a recursive formula for the cardinality of the degree class group of the members of this family. Moreover, we analyse the behaviour of the degree class group under standard geometrical operations on the curve, such as the blow up and the normalisation of a node.
Keywords
Cite
@article{arxiv.math/0602553,
title = {Combinatorial aspects of nodal curves},
author = {Simone Busonero and Margarida Melo and Lidia Stoppino},
journal= {arXiv preprint arXiv:math/0602553},
year = {2008}
}
Comments
28 pages, to appear in Le Matematiche. Revised version: minor changes, references added