Zobrazeno 1 - 10
of 229
pro vyhledávání: '"Siegel-Veech constants"'
We compute the asymptotic number of cylinders, weighted by their area to any non-negative power, on any cyclic branched cover of any generic translation surface in any stratum. Our formulas depend only on topological invariants of the cover and numbe
Externí odkaz:
http://arxiv.org/abs/2409.06600
We study the area Siegel-Veech constants of components of strata of abelian differentials with even or odd spin parity. We prove that these constants may be computed using either: (I) quasimodular forms, or (II) intersection theory. These results ref
Externí odkaz:
http://arxiv.org/abs/2210.17374
Publikováno v:
Journal of the American Mathematical Society, 2018 Oct 01. 31(4), 1059-1163.
Externí odkaz:
https://www.jstor.org/stable/90023954
Publikováno v:
Arnold Math. Journal, 6:2 (2020), 149-161
We state conjectures on the asymptotic behavior of the Masur-Veech volumes of strata in the moduli spaces of meromorphic quadratic differentials and on the asymptotics of their area Siegel-Veech constants as the genus tends to infinity.
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Externí odkaz:
http://arxiv.org/abs/1912.11702
Autor:
Aggarwal, Amol
Publikováno v:
Geom. Funct. Anal. 29, 1295-1324, 2019
In this paper we consider the large genus asymptotics for two classes of Siegel-Veech constants associated with an arbitrary connected stratum $\mathcal{H} (\alpha)$ of Abelian differentials. The first is the saddle connection Siegel-Veech constant $
Externí odkaz:
http://arxiv.org/abs/1810.05227
Autor:
Sauvaget, Adrien
In the 80's H. Masur and W. Veech defined two numerical invariants of strata of abelian differentials: the volume and the Siegel-Veech constant. Based on numerical experiments, A. Eskin and A. Zorich proposed a series of conjectures for the large gen
Externí odkaz:
http://arxiv.org/abs/1801.01744
Autor:
Dozier, Benjamin
We show that for any weakly convergent sequence of ergodic $SL_2(\mathbb{R})$-invariant probability measures on a stratum of unit-area translation surfaces, the corresponding Siegel-Veech constants converge to the Siegel-Veech constant of the limit m
Externí odkaz:
http://arxiv.org/abs/1701.00175
Quasimodular forms were first studied in the context of counting torus coverings. Here we show that a weighted version of these coverings with Siegel-Veech weights also provides quasimodular forms. We apply this to prove conjectures of Eskin and Zori
Externí odkaz:
http://arxiv.org/abs/1606.04065
Autor:
Eskin, Alex, Zorich, Anton
Publikováno v:
Arnold Mathematical Journal, 1:4 (2015) 481-488
We state conjectures on the asymptotic behavior of the volumes of moduli spaces of Abelian differentials and their Siegel-Veech constants as genus tends to infinity. We provide certain numerical evidence, describe recent advances and the state of the
Externí odkaz:
http://arxiv.org/abs/1507.05296
Autor:
Bauer, Max, Goujard, Elise
An Abelian differential gives rise to a flat structure (translation surface) on the underlying Riemann surface. In some directions the directional flow on the flat surface may contain a periodic region that is made up of maximal cylinders filled by p
Externí odkaz:
http://arxiv.org/abs/1405.4748