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Journal of the American Mathematical Society

Published by the American Mathematical Society, the Journal of the American Mathematical Society (JAMS) is devoted to research articles of the highest quality in all areas of pure and applied mathematics.

ISSN 1088-6834 (online) ISSN 0894-0347 (print)

The 2020 MCQ for Journal of the American Mathematical Society is 4.79.

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On Hitchin’s connection
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by Bert van Geemen and Aise Johan de Jong PDF
J. Amer. Math. Soc. 11 (1998), 189-228 Request permission

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
  • 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
  • Received by editor(s): January 16, 1997
  • Received by editor(s) in revised form: September 4, 1997
  • © Copyright 1998 American Mathematical Society
  • 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
  • MathSciNet review: 1469656