A local index theorem for families of $ \bar\partial$-operators on Riemann surfaces

DOI10.1070/RM1987v042n06ABEH001501zbMath0699.58061MaRDI QIDQ3477719

Peter Zograf, L. A. Takhtadzhyan

Publication date: 1987

Published in: Russian Mathematical Surveys (Search for Journal in Brave)

zbMATH Keywords

Riemannian surfacesQuillen metricTeichmüller theoryformulaharmonic Beltrami differentialAtiyah-Singer index

Mathematics Subject Classification ID

Moduli of Riemann surfaces, Teichmüller theory (complex-analytic aspects in several variables) (32G15) Index theory and related fixed-point theorems on manifolds (58J20) Riemann surfaces (30F99)

Related Items (9)

Differential geometry of moduli spaces of quiver bundles ⋮ Determinant bundle over the universal moduli space of vector bundles over the Teichmüller space ⋮ Determinant bundles, Quillen metrics and Mumford isomorphisms over the universal commensurability Teichmüller space ⋮ Holomorphic extensions of Laplacians and their determinants ⋮ Eta invariant and Selberg zeta function of odd type over convex co-compact hyperbolic manifolds ⋮ A local index theorem for families of \({\bar \partial}\)-operators on punctured Riemann surfaces and a new Kähler metric on their moduli spaces ⋮ Determinant bundle over the universal moduli space of principal bundles over the Teichmüller space ⋮ Coupled vortex equations and moduli: Deformation theoretic approach and Kähler geometry ⋮ Quillen connection and the uniformization of Riemann surfaces

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