Open Access
June 2004 Hitchin's Connection and Differential Operators with Values in the Determinant Bundle
Xiaotao Sun, I-Hsun Tsai
J. Differential Geom. 67(2): 335-376 (June 2004). DOI: 10.4310/jdg/1102536204


For a family of smooth curves, we have the associated family of moduli spaces of stable bundles with fixed determinant on the curves. There exists a so called theta line bundle on the family of moduli spaces. When the Kodaira–Spencer map of the family of curves is an isomorphism, we prove in this paper an identification theorem between sheaves of differential operators on the theta line bundle and higher direct images of vector bundles on curves. As an application, the so called Hitchin's connection on the direct image of (powers of) theta line bundle is derived naturally from the identification theorem. A logarithmic extension of Hitchin's connection to certain singular stable curves is also presented in this paper.


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Xiaotao Sun. I-Hsun Tsai. "Hitchin's Connection and Differential Operators with Values in the Determinant Bundle." J. Differential Geom. 67 (2) 335 - 376, June 2004.


Published: June 2004
First available in Project Euclid: 8 December 2004

zbMATH: 1120.14008
MathSciNet: MR2106127
Digital Object Identifier: 10.4310/jdg/1102536204

Rights: Copyright © 2004 Lehigh University

Vol.67 • No. 2 • June 2004
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