Good geometry on the curve moduli

DOI10.2977/prims/1210167341zbMath1219.14012OpenAlexW2001489661MaRDI QIDQ935918

Xiaofeng Sun, Ke Feng Liu, Shing Tung Yau

Publication date: 12 August 2008

Published in: Publications of the Research Institute for Mathematical Sciences, Kyoto University (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.2977/prims/1210167341

zbMATH Keywords

metricmoduli spaceRiemann surface

Mathematics Subject Classification ID

Global differential geometry of Hermitian and Kählerian manifolds (53C55) Complex-analytic moduli problems (32G13) Algebraic moduli problems, moduli of vector bundles (14D20) Singularities of curves, local rings (14H20)

Related Items (9)

Uniform bounds on harmonic Beltrami differentials and Weil-Petersson curvatures ⋮ On the Singular Set of Harmonic Maps into DM-Complexes ⋮ Growth of the Weil-Petersson inradius of moduli space ⋮ Curvature of the base manifold of a Monge-Ampère fibration and its existence ⋮ Riemann moduli spaces are quantum ergodic ⋮ Curvature properties for moduli of canonically polarized manifolds -- an analogy to moduli of Calabi-Yau manifolds ⋮ Spectral theory for the Weil-Petersson Laplacian on the Riemann moduli space ⋮ The Weil-Petersson curvature operator on the universal Teichmüller space ⋮ Positivity of relative canonical bundles and applications

Cites Work

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• Riemann's mapping theorem for variable metrics
• On the determinant of the bundle of meromorphic quadratic differentials on the Deligne-Mumford compactification of the moduli space of Riemann surfaces
• Canonical metrics on the moduli space of Riemann surfaces. II
• Harmonic maps of the moduli space of compact Riemann surfaces
• The extension of the Weil-Petersson metric to the boundary of Teichmüller space
• Hirzebruch's proportionality theorem in the non-compact case
• The irreducibility of the space of curves of a given genus
• Canonical metrics on the moduli space of Riemann surfaces. I
• Anti Self-Dual Yang-Mills Connections Over Complex Algebraic Surfaces and Stable Vector Bundles

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