Area Siegel--Veech constants for affine invariant submanifolds of REL zero

Dawei Chen; Elise Goujard; Martin Möller

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arXiv · 2504.03025

Area Siegel--Veech constants for affine invariant submanifolds of REL zero

Dawei Chen·Elise Goujard·Martin Möller

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Abstract

We describe the principal boundary of an arbitrary affine invariant submanifold of REL zero in terms of level graphs of the multi-scale compactification of strata of Abelian differentials with prescribed orders of zeros. We show that the area Siegel--Veech constant of the affine invariant submanifold can be obtained by using volumes of the principal boundary strata. As an application, we prove the conjectural formula in [CMS23a] that computes the area Siegel--Veech constant via intersection theory in the case of REL zero. In particular, the formula holds for strata of quadratic differentials with odd orders of zeros and for the gothic locus. We also explicitly describe the principal boundary components of the gothic locus and their individual contributions to the area Siegel--Veech constant

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Dawei Chen, Elise Goujard, Martin Möller. 2025-04-03. Area Siegel--Veech constants for affine invariant submanifolds of REL zero. https://arxiv.org/abs/2504.03025

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