The cohomology of line bundles of splice-quotient singularities

Details The cohomology of line bundles of splice-quotient singularities The cohomology of line bundles of splice-quotient singularities

2008-10-22

arxiv.org/abs/0810.4129v1

Mathematics

Algebraic Geometry

16 pages

Scientific paper

We provide several results on splice-quotient singularities: a combinatorial expression of the dimension of the first cohomology of all `natural' line bundles, an equivariant Campillo-Delgado-Gusein-Zade type formula about the dimension of relative sections of line bundles (proving that the equivariant, divisorial multi-variable Hilbert series is topological), a combinatorial description of divisors of analytic function-germs, and an expression for the multiplicity of the singularity from its resolution graph. Additional, we establish a new formula for the Seiberg-Witten invariants of any rational homology sphere singularity link.

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