Nodal curves on surfaces of general type

Details Nodal curves on surfaces of general type Nodal curves on surfaces of general type

1996-02-14

arxiv.org/abs/alg-geom/9602012v1

Mathematics

Algebraic Geometry

15 pages, AMSTeX

Scientific paper

We study the family of irreducible curves with $\delta$ nodes belonging to a free linear system $|C|$ with smooth general member on a surface $S$ such that $|K_S|$ is ample. Under the assumption that $C$ is numerically equivalent to $pK_S$, $p\ge 3$ rational, we give an upper bound on $\delta$ ensuring that the family is smooth of codimension $\delta$ in $|C|$ (plus another slightly different result of the same type). We give examples showing that the bound is sharp. Some related results concerning linear normality of nodal curves are proved.

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