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arXiv · 2202.07250

Tropical curves in abelian surfaces I: enumeration of curves passing through points

Thomas Blomme
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Abstract

This paper is the first part in a series of three papers devoted to the study of enumerative invariants of abelian surfaces through the tropical approach. In this paper, we consider the enumeration of genus $g$ curves of fixed degree passing through $g$ points. We compute the multiplicity provided by a correspondence theorem due to T. Nishinou and show that it is possible to refine this multiplicity in the style of Block-G\"ottsche to get tropical refined invariants.

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Thomas Blomme. 2022-02-15. Tropical curves in abelian surfaces I: enumeration of curves passing through points. https://doi.org/10.1017/s0305004124000161

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