Cusps and the family hyperbolic metric

DOI10.1215/S0012-7094-07-13833-XzbMath1144.14029arXivmath/0508470MaRDI QIDQ997102

Scott A. Wolpert

Publication date: 20 July 2007

Published in: Duke Mathematical Journal (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/math/0508470

zbMATH Keywords

Riemann surfacesholomorphic line bundleshyperbolic metricsholomorphic family

Mathematics Subject Classification ID

Moduli of Riemann surfaces, Teichmüller theory (complex-analytic aspects in several variables) (32G15) Vector bundles on curves and their moduli (14H60) Teichmüller theory for Riemann surfaces (30F60) Families, moduli of curves (analytic) (14H15)

Related Items

Spanning trees, cycle-rooted spanning forests on discretizations of flat surfaces and analytic torsion ⋮ Potentials and Chern forms for Weil-Petersson and Takhtajan-Zograf metrics on moduli spaces ⋮ An arithmetic Hilbert-Samuel theorem for pointed stable curves ⋮ Analytic torsion for surfaces with cusps. I: Compact perturbation theorem and anomaly formula ⋮ A tour through Mirzakhani’s work on moduli spaces of Riemann surfaces ⋮ Analytic torsion for surfaces with cusps. II: Regularity, asymptotics and curvature theorem ⋮ Grafting hyperbolic metrics and Eisenstein series ⋮ Local index theorem for orbifold Riemann surfaces ⋮ The first Chern form on moduli of parabolic bundles ⋮ The arithmetic Riemann-Roch theorem and the Jacquet-Langlands correspondence ⋮ Virtual neighborhood technique for moduli spaces of holomorphic curves ⋮ The asymptotic behavior of the Takhtajan-Zograf metric ⋮ Gluing Principle for Orbifold Stratified Spaces ⋮ Products of twists, geodesic lengths and Thurston shears ⋮ A local families index formula for \({\overline{\partial}}\)-operators on punctured Riemann surfaces ⋮ Central charge from adiabatic transport of cusp singularities in the quantum Hall effect

Cites Work

• Riemann's mapping theorem for variable metrics
• On the Kähler form of the moduli space of once punctured tori
• Simple geodesics and Weil-Petersson volumes of moduli spaces of bordered Riemann surfaces
• The hyperbolic metric and the geometry of the universal curve
• Grafting hyperbolic metrics and Eisenstein series
• On the symplectic geometry of deformations of a hyperbolic surface
• On the homology of the moduli space of stable curves
• Chern forms and the Riemann tensor for the moduli space of curves
• The Teichmüller theory of harmonic maps
• The Fenchel-Nielsen deformation
• Intersection theory on the moduli space of curves and the matrix Airy function
• Two dimensional gauge theories revisited
• Schiffer's interior variation and quasiconformal mapping
• The extension of the Weil-Petersson metric to the boundary of Teichmüller space
• Stability of projective varieties
• Disappearance of cusp forms in special families
• Moment maps and combinatorial invariants of Hamiltonian \(T^ n\)-spaces
• Non-completeness of Zograf-Takhtajan's Kähler metric for Teichmüller space of punctured Riemann surfaces
• A local index theorem for families of \({\bar \partial}\)-operators on punctured Riemann surfaces and a new Kähler metric on their moduli spaces
• The asymptotic behavior of the Takhtajan-Zograf metric
• Some remarks on Teichmüller's space of Riemann surfaces
• Über Spitzen diskontinuierlicher Gruppen von lineargebrochenen Transformationen
• Weil-Petersson volumes and intersection theory on the moduli space of curves
• An algebro-geometric proof of Witten’s conjecture
• On the Weil-Petersson Geometry of the Moduli Space of Curves
• Combinatorial and algebro-geometric cohomology classes on the moduli spaces of curves
• Fourier coefficients of the resolvent for a Fuchsian group.
• Classification of Weil-Petersson isometries
• \(\Omega\)-admissible theory. II: Deligne pairings over moduli spaces of punctured Riemann surfaces
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item

This page was built for publication: Cusps and the family hyperbolic metric