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arXiv · 2604.26000

Cut and paste invariants of moduli spaces of stable maps to toric surfaces

Cat Rust
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Abstract

We study moduli spaces of logarithmic stable maps to proper toric surfaces with prescribed tangency conditions to the toric boundary. Fixing a surface, we define a chamber decomposition on the space of all tangencies such that as a function of the tangency data, the class of the corresponding moduli space in the Grothendieck ring of varieties is constant. The tangency data defines a collection of lines through the origin which, along with the rays of the toric fan, are cyclically ordered. The chambers of the decomposition are regions for which this cyclic ordering is constant and generalise the well-known resonance chambers. We pose the open question of whether the Gromov-Witten invariants of the moduli spaces are polynomial on these chambers.

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Cat Rust. 2026-04-28. Cut and paste invariants of moduli spaces of stable maps to toric surfaces. https://arxiv.org/abs/2604.26000

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