Large-genus asymptotics of saddle connection Siegel-Veech constants

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.

Publication Details

Journal
ArXiv.org
Published
2025-05-29
Primary Topic
Mathematical Dynamics and Fractals
Type
article
Field-Weighted Citation Impact
0.00

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article

Large-genus asymptotics of saddle connection Siegel-Veech constants

ArXiv.org
Mathematical Dynamics and Fractals
article

Large-genus asymptotics of saddle connection Siegel-Veech constants

article en

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.

ArXiv.org
Deutsche Forschungsgemeinschaft
Openalex Percentile: Top 44%
Mathematical Dynamics and Fractals
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Large-genus asymptotics of saddle connection Siegel-Veech constants · ArXiv.org (2025) | TGRS Research Map | TGRS