Large-genus asymptotics of saddle connection Siegel-Veech constants

Anja Randecker

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arXiv · 2505.23711

Large-genus asymptotics of saddle connection Siegel-Veech constants

Anja Randecker

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Abstract

Siegel-Veech constants are powerful tools for counting saddle connections on a translation surface. Their computation can be involved, most famously with recursive formulas that use intricate combinatorics or intersection theory. From these formulas, asymptotics of Siegel-Veech constants for growing genus can be extracted. We extend the known asymptotics to all strata and to all multiplicities of saddle-connections between distinct zeros and of loops.

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Anja Randecker. 2025-05-29. Large-genus asymptotics of saddle connection Siegel-Veech constants. https://arxiv.org/abs/2505.23711

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