Masur-Veech volumes of quadratic differentials and their asymptotics. (English) Zbl 1452.14034
Let \(\mathcal Q_{g,n}\) be the moduli space of quadratic differentials on genus \(g\) Riemann surfaces with at worst simple poles at the \(n\) marked points. It carries a natural volume form given by period coordinates with respect to the induced flat metric, and the associate volume \(\mathrm{Vol}~\mathcal Q_{g,n}\) (after suitable normalization) is called the Masur-Veech volume of the principal strata of quadratic differentials. In [“Masur-Veech volumes and intersection theory: the principal strata of quadratic differentials”, Preprint, arXiv:1912.02267] D. Chen et al. gave an expression of \(\mathrm{Vol}~\mathcal Q_{g,n}\) via certain linear Hodge integrals on the Deligen-Mumford moduli space of curves. Based on this formula, the authors apply the theory of integrable systems to derive a number of relations for the generating series of \(\mathrm{Vol}~\mathcal Q_{g,n}\). Moreover, they provide refinements of the conjectural formulas given in [A. Aggarwal et al., Arnold Math. J. 6, No. 2, 149–161 (2020; Zbl 1452.14026)] for the large genus asymptotics of the \(\mathrm{Vol}~\mathcal Q_{g,n}\) as well as the associated area Siegel-Veech constants. As a remark, the original version of the large genus asymptotic conjecture for \(\mathrm{Vol}~\mathcal Q_{g,n}\) has been recently setted by A. Aggarwal [“Large genus asymptotics for intersection numbers and principal strata volumes of quadratic differentials”, Preprint, arXiv:2004.05042].
Reviewer: Dawei Chen (Chestnut Hill)
MSC:
| 14H81 | Relationships between algebraic curves and physics |
| 14H10 | Families, moduli of curves (algebraic) |
| 14H15 | Families, moduli of curves (analytic) |
| 32G15 | Moduli of Riemann surfaces, Teichmüller theory (complex-analytic aspects in several variables) |
| 30F30 | Differentials on Riemann surfaces |
Keywords:
Masur-Veech volumes; ILW hierarchy; linear Hodge integrals; area Siegel-Veech constants; large genus asymptotics; moduli spaceCitations:
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