Large-genus asymptotics of saddle connection Siegel-Veech constants

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.

52 pages, 1 figure, 1 table; v2: completely rewritten, extended results and fixed errors, changed authors and title; v1: 28 pages, 1 figure, 1 table