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

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-Göttsche to get tropical refined invariants.

37 pages, 14 figures, comments welcome

References in corpus (4)

• On refined count of rational tropical curves
• Refined count of real oriented rational curves
• Floor diagrams and enumerative invariants of line bundles over an elliptic curve
• Tropical curves in abelian surfaces III: pearl diagrams and multiple cover formulas