The geometric genus of normal surface singularities

The geometric genus of normal surface singularities

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András Némethi , Alfréd Rényi Institute of Mathematics
Fine Hall 322

We discuss several topological characterizations of the geometric genus of a complex normal surface singularity under certain topological and analytic restrictions. The `classical' cases include the rational and elliptic singularities. More recent characterizations in terms of the Seiberg-Witten invariant and lattice cohomology of the link include more general classes (weighted homogeneous, splice quotients). In terms of the multi-variable divisorial filtration we explain how the Seiberg-Witten invariant appears naturally, and we provide some motivation for the definition of the lattice cohomology as well.