Moduli of nodal curves on smooth surfaces of general type

Details Moduli of nodal curves on smooth surfaces of general type Moduli of nodal curves on smooth surfaces of general type

2001-03-29

arxiv.org/abs/math/0103205v1

Mathematics

Algebraic Geometry

Latex2e, 27 pages

Scientific paper

In this paper we focus on the problem of computing the number of moduli of the so called Severi varieties (denoted by V(|D|, \delta)), which parametrize universal families of irreducible, \delta-nodal curves in a complete linear system |D|, on a smooth projective surface S of general type. We determine geometrical and numerical conditions on D and numerical conditions on \delta ensuring that such number coincides with dim(V(|D|, \delta). As related facts, we also determines some sharp results concerning the geometry of some Severi varieties.

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