Geodesic
On Hitchin’s connection
van Geemen, Bert 1   ; de Jong, Aise Johan 2
1 Dipartimento di Matematica, Università di Torino, Via Carlo Alberto 10, 10123 Torino, Italy
2 Department of Mathematics, Princeton University, Fine Hall – Washington Road, Princeton, New Jersey 08544-1000
Journal of the American Mathematical Society, Tome 11 (1998) no. 1, pp. 189-228 Cet article a éte moissonné depuis la source American Mathematical Society

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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.
DOI : 10.1090/S0894-0347-98-00252-5

van Geemen, Bert  1   ; de Jong, Aise Johan  2

1 Dipartimento di Matematica, Università di Torino, Via Carlo Alberto 10, 10123 Torino, Italy
2 Department of Mathematics, Princeton University, Fine Hall – Washington Road, Princeton, New Jersey 08544-1000 
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van Geemen, Bert; de Jong, Aise Johan. On Hitchin’s connection. Journal of the American Mathematical Society, Tome 11 (1998) no. 1, pp. 189-228. doi: 10.1090/S0894-0347-98-00252-5

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