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

DOI:
https://doi.org/10.1090/S0894-0347-98-00252-5

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Abstract | References | Similar Articles | Additional Information

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

Email:
geemen@dm.unito.it

**Aise Johan de Jong**

Affiliation:
Department of Mathematics, Princeton University, Fine Hall – Washington Road, Princeton, New Jersey 08544-1000

Email:
dejong@math.Princeton.EDU

DOI:
https://doi.org/10.1090/S0894-0347-98-00252-5

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