Irreducibility of Equisingular Families of Curves - Improved Conditions

Details Irreducibility of Equisingular Families of Curves - Improved Conditions Irreducibility of Equisingular Families of Curves - Improved Conditions

2002-12-05

arxiv.org/abs/math/0212090v1

Comm. Algebra 33 (2005), no. 2, 455--466

Mathematics

Algebraic Geometry

This article uses the notation introduced in math.AG/0108089, and many results proved there. 12 pages

Scientific paper

In math.AG/0108089 we gave sufficient conditions for the irreducibility of the family V of irreducible curves in the linear system |D| with precisely r singular points of topological respectively analytical types S1,...,Sr on several classes of smooth projective surfaces S. The conditions where of the form (tau'(S1)+2)^2 +...+ (tau'(Sr)+2)^2 < c*(D-K)^2, where tau' is some invariant of singularity types, K is the canonical divisor of S and c is some constant. In the present paper we improve this condition, that is the constant c, by a factor 9.

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