Variation of Hodge structure and enumerating tilings of surfaces by triangles and squares

DOI10.5802/jep.159zbMath1466.14032arXiv2007.04185OpenAlexW3143892120MaRDI QIDQ2028048

Vincent Koziarz, Duc-Manh Nguyen

Publication date: 31 May 2021

Published in: Journal de l'École Polytechnique -- Mathématiques (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/2007.04185

zbMATH Keywords

differentials on Riemann surfacesvariation of Hodge structureMasur-Veech volumemoduli spaces of flat surfacestilings of surfaces

Mathematics Subject Classification ID

Moduli of Riemann surfaces, Teichmüller theory (complex-analytic aspects in several variables) (32G15) Tilings in (2) dimensions (aspects of discrete geometry) (52C20) Families, moduli of curves (analytic) (14H15) Differentials on Riemann surfaces (30F30)

Related Items (4)

Masur-Veech volumes, frequencies of simple closed geodesics, and intersection numbers of moduli spaces of curves ⋮ Dynamical invariants and intersection theory on the flex and gothic loci ⋮ Counting tripods on the torus ⋮ Intersection theory and volumes of moduli spaces of flat metrics on the sphere

Cites Work

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• Splitting mixed Hodge structures over affine invariant manifolds
• Isolation, equidistribution, and orbit closures for the \(\mathrm{SL}(2,\mathbb{R})\) action on moduli space
• Volumes of strata of moduli spaces of quadratic differentials: getting explicit values
• Moduli spaces of quadratic differentials
• Linear manifolds in the moduli space of one-forms
• Variation of Hodge structure: The singularities of the period mapping
• Connected components of the moduli spaces of Abelian differentials with prescribed singularities
• Volumes and Siegel-Veech constants of \({\mathcal{H}}(2G - 2)\) and Hodge integrals
• The number of convex tilings of the sphere by triangles, squares, or hexagons
• Invariant and stationary measures for the \(\mathrm{SL}(2,\mathbb{R})\) action on moduli space
• Symplectic and isometric \(\mathrm{SL}(2,\mathbb{R})\)-invariant subbundles of the Hodge bundle
• Symmetric differentials and variations of Hodge structures
• Minimal sets for flows on moduli space
• Compactification of strata of abelian differentials
• Hurwitz theory of elliptic orbifolds. I
• Cubic curves and totally geodesic subvarieties of moduli space
• The field of definition of affine invariant submanifolds of the moduli space of abelian differentials
• Théorie de Hodge. II. (Hodge theory. II)
• Equations différentielles à points singuliers réguliers
• Right-angled billiards and volumes of moduli spaces of quadratic differentials on CP^1
• The Gauss-Bonnet theorem for cone manifolds and volumes of moduli spaces
• Complex hyperbolic volume and intersection of boundary divisors in moduli spaces of genus zero curves
• Masur–Veech volume of the gothic locus
• Strata of $k$-differentials
• Asymptotics of numbers of branched coverings of a torus and volumes of moduli spaces of holomorphic differentials

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