Combinatorial aspects of nodal curves
Abstract
To any nodal curve C one associates its degree class group, a combinatorial invariant which plays an important role in the compactification of the generalized Jacobian of C and in the construction of the Néron model of the Picard variety of families of curves having C as special fibre. In this paper we study this invariant.More precisely, we construct a 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 the 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 normalization of a node.
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