Universal polynomials for singular curves on surfaces

Details Universal polynomials for singular curves on surfaces Universal polynomials for singular curves on surfaces

2012-03-14

arxiv.org/abs/1203.3180v1

Mathematics

Algebraic Geometry

12 pages

Scientific paper

Let S be a complex smooth projective surface and L be a line bundle on S. For any given collection of isolated topological or analytic singularity types, we show the number of curves in the linear system |L| with prescribed singularities is a universal polynomial of Chern numbers of L and S, assuming L is sufficiently ample. Moreover, we define a generating series whose coefficients are these universal polynomials and discuss its properties. This work is a generalization of Gottsche's conjecture to curves with higher singularities.

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