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arXiv · 2309.06995

Tropical M\"obius strips and ruled surfaces

Thomas Blomme·Victoria Schleis
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Abstract

We consider the enumeration of tropical curves in M\"obius 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.

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Thomas Blomme, Victoria Schleis. 2023-09-13. Tropical M\"obius strips and ruled surfaces. https://arxiv.org/abs/2309.06995

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