Remarks on the geometry of moduli spaces

DOI10.1090/S0002-9939-96-03046-8zbMath0873.14031MaRDI QIDQ4875514

Ke Feng Liu

Publication date: 2 November 1997

Published in: Proceedings of the American Mathematical Society (Search for Journal in Brave)

zbMATH Keywords

Schwarz lemmaTeichmüller spacesmoduli of curvesstable curvesdualizing sheafHodge bundleQuillen metricsPetersson-Weil metricdeterminant bundles

Mathematics Subject Classification ID

Families, moduli of curves (algebraic) (14H10) Moduli of Riemann surfaces, Teichmüller theory (complex-analytic aspects in several variables) (32G15) Algebraic moduli problems, moduli of vector bundles (14D20) Families, moduli of curves (analytic) (14H15)

Related Items (2)

Remarks on BCOV invariants and degenerations of Calabi-Yau manifolds ⋮ Complex geometry: its brief history and its future

Cites Work

• The hyperbolic metric and the geometry of the universal curve
• Determinant fiber bundles, Quillen metric and degeneracy of curves.
• On the homology of the moduli space of stable curves
• Arakelov's theorem for abelian varieties
• Chern forms and the Riemann tensor for the moduli space of curves
• Potential of the Weil-Petersson metric on the Torelli space
• Kähler hyperbolicity and \(L_ 2\)-Hodge theory
• On Obtaining a Positive Line Bundle from the Weil-Petersson Class
• A General Schwarz Lemma for Kahler Manifolds
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