Invariants of generic normal surface singularities

András Némethi
University of Budapest (ELTE), Hungary
https://users.renyi.hu/~nemethi/pub.html

Date(s) : 21/01/2021   iCal
14 h 00 min - 15 h 00 min

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 surfacesingularities.

https://arxiv.org/abs/1910.03275

Slides: https://eta.impa.br/icm_files/invited/section_6/IL.6.4.pdf

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