Tropical M\"obius strips and ruled surfaces
Thomas Blomme, Victoria Schleis

TL;DR
This paper explores the enumeration of tropical curves in M"obius strips and their relation to rational ruled surfaces, establishing regularity properties and modularity of associated generating series.
Contribution
It introduces a novel correspondence between tropical curves in M"obius strips and curves in rational ruled surfaces, proving new regularity and modularity results.
Findings
Piecewise quasi-polynomiality of relative invariants
Quasi-modularity of generating series
Relation between tropical curves and algebraic surfaces
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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Taxonomy
TopicsPolynomial and algebraic computation · Algebraic Geometry and Number Theory · Commutative Algebra and Its Applications
