Volumes of strata of abelian differentials and Siegel-Veech constants in large genera. (English) Zbl 1342.32012
In recent years, the dynamics and geometry of the moduli space of abelian differentials (pairs \((X, \omega)\), where \(X\) is a compact genus-\(g\) Riemann surface and \(\omega\) a holomorphic one-form) have been objects of active study. These spaces are stratified by integer partitions of \(2g-2\) which describe the patterns of zeros of the one-forms \(\omega\). The paper under review states an important conjecture on the asymptotics of the volumes of these strata for \(g \rightarrow \infty\) (the volumes are defined by period coordinates, and are shown to be finite by Masur and Veech), which has subsequently been proved by Chen-Moeller-Zagier.
Reviewer: Jayadev Athreya (Seattle)
MSC:
| 32G15 | Moduli of Riemann surfaces, Teichmüller theory (complex-analytic aspects in several variables) |
| 30F60 | Teichmüller theory for Riemann surfaces |
References:
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