Tropical Möbius strips and ruled surfaces

Abstract

We consider the enumeration of tropical curves in Möbius strips for two different lattice structures and relate them to the enumeration of curves in two rational ruled surfaces over a complex elliptic curve. Using this correspondence, we prove regularity results such as the piecewise quasi-polynomiality of relative invariants and the quasi-modularity of their generating series.

arXiv comment39 pages, comments welcome