Asymptotics of numbers of branched coverings of a torus and volumes of moduli spaces of holomorphic differentials
From MaRDI portal
Publication:5944969
DOI10.1007/s002220100142zbMath1019.32014arXivmath/0006171OpenAlexW2024810567WikidataQ112631892 ScholiaQ112631892MaRDI QIDQ5944969
Publication date: 15 September 2003
Published in: Inventiones Mathematicae (Search for Journal in Brave)
Full work available at URL: https://arxiv.org/abs/math/0006171
Combinatorial aspects of partitions of integers (05A17) Moduli of Riemann surfaces, Teichmüller theory (complex-analytic aspects in several variables) (32G15)
Related Items (78)
Masur-Veech volumes, frequencies of simple closed geodesics, and intersection numbers of moduli spaces of curves ⋮ Parity of the spin structure defined by a quadratic differential ⋮ Teichmüller geodesics of infinite complexity. ⋮ Fuchsian groups, coverings of Riemann surfaces, subgroup growth, random quotients and random walks. ⋮ Volumes and Siegel-Veech constants of \({\mathcal{H}}(2G - 2)\) and Hodge integrals ⋮ Statistics of Square-Tiled Surfaces: Symmetry and Short Loops ⋮ QUASIMODULAR FORMS AND COHOMOLOGY ⋮ Asymptotic identities for additive convolutions of sums of divisors ⋮ The topology and geometry of random square-tiled surfaces ⋮ Prime arithmetic Teichmüller discs in \({\mathcal H}(2)\) ⋮ Origamis associated to minimally intersecting filling pairs ⋮ Triply mixed coverings of arbitrary base curves: quasimodularity, quantum curves and a mysterious topological recursion ⋮ Stein’s method and Plancherel measure of the symmetric group ⋮ Covers of the projective line and the moduli space of quadratic differentials ⋮ Pillowcase covers: counting Feynman-like graphs associated with quadratic differentials ⋮ Quasimodularity and large genus limits of Siegel-Veech constants ⋮ On the topology of \(\mathcal{H}(2)\) ⋮ Square-tiled tori ⋮ Quasimodular forms and quasimodular polynomials ⋮ Non‐planarity of SL(2,Z)$\operatorname{SL}(2,\mathbb {Z})$‐orbits of origamis in H(2)$\mathcal {H}(2)$ ⋮ Symmetric tensor representations, quasimodular forms, and weak Jacobi forms ⋮ Nonvarying sums of Lyapunov exponents of abelian differentials in low genus ⋮ Siegel-Veech constants for strata of moduli spaces of quadratic differentials ⋮ An extended trace formula for vertex operators ⋮ Stein's method and random character ratios ⋮ Topological recursion for Masur–Veech volumes ⋮ Contribution of \(n\)-cylinder square-tiled surfaces to Masur-Veech volume of \(\mathcal{H}(2g-2)\) ⋮ Masur-Veech volumes and intersection theory: the principal strata of quadratic differentials. With an appendix by Gaëtan Borot, Alessandro Giacchetto and Danilo Lewanski ⋮ Large genus bounds for the distribution of triangulated surfaces in moduli space ⋮ Intersection theory and volumes of moduli spaces of flat metrics on the sphere ⋮ Billiards in rectangles with barriers ⋮ Energy functions on moduli spaces of flat surfaces with erasing forest ⋮ Square-tiled surfaces and rigid curves on moduli spaces ⋮ Parallelogram decompositions and generic surfaces in \(\mathcal H^{\text{hyp}}(4)\) ⋮ Conjectural large genus asymptotics of Masur-Veech volumes and of area Siegel-Veech constants of strata of quadratic differentials ⋮ Two-dimensional Yang-Mills theory and moduli spaces of holomorphic differentials ⋮ On the error bound in the normal approximation for Jack measures ⋮ Moduli spaces of Abelian differentials: the principal boundary, counting problems, and the Siegel-Veech constants ⋮ Large genus asymptotics for volumes of strata of abelian differentials ⋮ Cardinality of Rauzy classes ⋮ Counting formulae for square-tiled surfaces in genus two ⋮ Counting generalized Jenkins-Strebel differentials ⋮ Masur–Veech volume of the gothic locus ⋮ Sum of Lyapunov exponents of the Hodge bundle with respect to the Teichmüller geodesic flow ⋮ Convergence of Siegel-Veech constants ⋮ THE MODULI SPACE OF TWISTED CANONICAL DIVISORS ⋮ Euler characteristics of Teichmüller curves in genus two ⋮ Volumes of strata of moduli spaces of quadratic differentials: getting explicit values ⋮ The theta characteristic of a branched covering ⋮ Modular polynomials and derivatives of quasimodular forms ⋮ Geometry of periodic regions on flat surfaces and associated Siegel-Veech constants ⋮ The law of the iterated logarithm for character ratios ⋮ Characterizations of lattice surfaces ⋮ An Algorithm for Finding the Veech Group of an Origami ⋮ Masur-Veech volumes and intersection theory on moduli spaces of abelian differentials ⋮ On the finite blocking property ⋮ Stein's method, Jack measure, and the Metropolis algorithm ⋮ Dirichlet series of Rankin-Cohen brackets ⋮ Counting square-tiled surfaces with prescribed real and imaginary foliations and connections to Mirzakhani's asymptotics for simple closed hyperbolic geodesics ⋮ Triangulations and volume form on moduli spaces of flat surfaces ⋮ Billiard dynamics: An updated survey with the emphasis on open problems ⋮ Billiards and Teichmüller curves on Hilbert modular surfaces ⋮ Variation of Hodge structure and enumerating tilings of surfaces by triangles and squares ⋮ Book Review: Twisted Teichmüller curves ⋮ Covers of elliptic curves and the moduli space of stable curves ⋮ Volumes of strata of abelian differentials and Siegel-Veech constants in large genera ⋮ Quasimodular forms and Jacobi-like forms ⋮ Orbit classification and asymptotic constants for 𝑑-symmetric covers ⋮ Large genus asymptotics for intersection numbers and principal strata volumes of quadratic differentials ⋮ Regularized integrals on Riemann surfaces and modular forms ⋮ Martingales and character ratios ⋮ QUASIMODULAR FORMS AND VECTOR BUNDLES ⋮ Teichm\"uller dynamics in the eyes of an algebraic geometer ⋮ When is the Bloch-Okounkov \(q\)-bracket modular? ⋮ Single-cylinder square-tiled surfaces and the ubiquity of ratio-optimising pseudo-Anosovs ⋮ Large genus asymptotics for Siegel-Veech constants ⋮ Teichmüller curves in genus two: Discriminant and spin ⋮ Introduction to Teichmüller theory and its applications to dynamics of interval exchange transformations, flows on surfaces and billiards
This page was built for publication: Asymptotics of numbers of branched coverings of a torus and volumes of moduli spaces of holomorphic differentials
