Invariants of generic normal surface singularities

Andras Nemethi (MTA Rényi Institute of Mathematics)

Monday 10th May 16:00-17:00 Online

Abstract

We fix a topological type of a complex analytic normal surface singularity, and will assume that the corresponding link (as oriented compact 3-manifold) is a rational homology sphere (equivalently, the resolution graph is a tree of rational vertices). This topological type might support several rather different analytic structures, in this talk we will consider a generic one (in the sense of Laufer). One can expect that several discrete analytic invariants can be read concretely from the resolution  graph: we will present such topological characterizations for the geometric genus, for cohomology groups of certain (natural) line bundles, analytic semigroup, maximal ideal cycle, multiplicity. The work is part a joint work and project with Janos Nagy. The main tool is the generalization of the Abel map to the case of normal surface singularities.


The talk will be preceded by a tea time at 3:45pm. The Zoom link for the seminar is https://uofglasgow.zoom.us/j/91412568415 and the passcode is the genus of the two-dimensional sphere (4 letters, all lowercase).


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