Multiplicity-one support for area Siegel–Veech constants of quadratic-differential strata

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Let Π^4g−4\hat\Pi_{4g-4} be the set of partitions of 4g−44g-4 with parts in {−1,0,1,2,… }\{-1,0,1,2,\dots\} and at most log⁡(g)\log(g) entries equal to −1-1. For a stratum Q(d1,…,dn){\mathcal Q}(d_1,\dots,d_n) with (d1,…,dn)∈Π^4g−4(d_1,\dots,d_n)\in\hat\Pi_{4g-4}, let carea(Q(d1,…,dn))c_{\mathit{area}}({\mathcal Q}(d_1,\dots,d_n)) be its area Siegel–Veech constant. For di,dj≥1d_i,d_j\geq1 with i≠ji\neq j and {di,dj}⊂{d1,…,dn}\{d_i,d_j\}\subset\{d_1,\dots,d_n\}, and for a1,a2≥0a_1,a_2\geq0 satisfying a1+a2≥3a_1+a_2\geq3 and a1+a2+2∈{d1,…,dn}a_1+a_2+2\in\{d_1,\dots,d_n\}, denote the relevant configurations by Cb,I(di,dj)\mathcal C_{b,\mathrm I}(d_i,d_j) and Cb,II(a1,a2)\mathcal C_{b,\mathrm{II}}(a_1,a_2). Multiplicity-one support conjecture. For all such strata, the Siegel–Veech constant is asymptotically supported on the configurations Cb,I(di,dj)\mathcal C_{b,\mathrm I}(d_i,d_j) and Cb,II(a1,a2)\mathcal C_{b,\mathrm{II}}(a_1,a_2). The statement concerns the asymptotic contribution of these configurations and is presented without a resolution in the supplied text.

References

Primary source

Amol Aggarwal, Vincent Delecroix, Elise Goujard, Peter Zograf and Anton Zorich, “Conjectural large genus asymptotics of Masur-Veech volumes and of area Siegel-Veech constants of strata of quadratic differentials”, arXiv:1912.11702 (2019).

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