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On Hitchin's connection
Author(s):
Bert
van Geemen;
Aise
Johan
de Jong
Journal:
J. Amer. Math. Soc.
11
(1998),
189-228.
MSC (1991):
Primary 14H60, 53C05;
Secondary 20F36, 32G15, 14D20
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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
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:
10.1090/S0894-0347-98-00252-5
PII:
S 0894-0347(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
Copyright of article:
Copyright
1998,
American Mathematical Society
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