Class of images of Abel maps on normal surface singularities

TL;DR

This paper studies Abel maps on normal surface singularities, focusing on the projective closure of their images, and provides explicit formulas and bounds for associated invariants, enhancing understanding of their geometric properties.

Contribution

It introduces a detailed analysis of Abel map images on normal surface singularities, including explicit combinatorial formulas and bounds for their invariants.

Findings

Explicit combinatorial formulas for invariants in generic cases

Upper bounds for invariants in general cases

Insights into the geometry of Abel map images on singularities

Abstract

In this paper we investigate Abel maps on normal surface singularities described in \cite{NNI}. We investigate the affine version of the class of the images of Abel maps on normal surface singularities. More precisely we consider the projective clousure of the image of an Abel map, its dual projective variety and we substract from its degree the multiplicity of the infinite hyperplane on the dual variety. In the case of generic singularities we prove explicit combinatorial formulas of this invariant, in the general case we prove an upper bound.