Kernel functions, analytic torsion and moduli spaces

This work investigates analytic torsion on the moduli space of degree zero stable bundles on a compact Reimann surface. Zeta-function regularization and perturbation-curvature formulas for torsion are developed using a modified resolvent-Szego kernel. The author discusses the bosonization formulas o...

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Bibliographic Details
Main Author: Fay, John D. (John David)
Format: eBook Book
Language:English
Published: Providence, R.I American Mathematical Society 1992
Edition:1
Series:Memoirs of the American Mathematical Society
Subjects:
Functions, Theta
Kernel functions
Moduli theory
ISBN:9780821825501, 082182550X
Online Access:Get full text
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Table of Contents:
  • Intro -- Table of Contents -- Introduction -- 1. Theta Functions -- Determinants and the Mumford form -- Arakelov-Faltings metrics -- 2. Kernel Functions and Analytic Torsion -- Szegö kernel for a hermitian bundle -- Resolvent kernel -- determinant of the laplacian -- 3. Variational Formulas -- Perturbation of resolvent and kernel functions -- Perturbation of torsion -- curvature formulas -- 4. Torsion on the Moduli Space of Stable Bundles -- Complex structure on the moduli space -- Torsion and non-abelian theta-functions -- 5. Torsion on Teichmuller Space -- Heat equations -- Insertion theorems -- Notational Index -- References