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On Hitchin’s connection

Authors: Bert van Geemen and Aise Johan de Jong
Journal: J. Amer. Math. Soc. 11 (1998), 189-228
MSC (1991): Primary 14H60, 53C05; Secondary 20F36, 32G15, 14D20
MathSciNet review: 1469656
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Abstract: The aim of the paper is to give an explicit expression for Hitchin’s connection in the case of stable rank 2 bundles on genus 2 curves. Some general theory (in the algebraic geometric setting) concerning heat operators is developed. In particular the notion of compatibility of a heat operator with respect to a closed subvariety is introduced. This is used to compare the heat operator in the nonabelian rank 2 genus 2 case to the abelian heat operator (on theta functions) for abelian surfaces. This relation allows one to perform the computation; the resulting differential equations are similar to the Knizhnik-Zalmolodshikov equations.

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Additional Information

Bert van Geemen
Affiliation: Dipartimento di Matematica, Università di Torino, Via Carlo Alberto 10, 10123 Torino, Italy
MR Author ID: 214021

Aise Johan de Jong
Affiliation: Department of Mathematics, Princeton University, Fine Hall – Washington Road, Princeton, New Jersey 08544-1000
Email: dejong@math.Princeton.EDU

Keywords: Hitchin’s connection, moduli of vector bundles, heat equations, heat operators
Received by editor(s): January 16, 1997
Received by editor(s) in revised form: September 4, 1997
Article copyright: © Copyright 1998 American Mathematical Society