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JACOBI COHOMOLOGY, LOCAL GEOMETRY OF MODULI SPACES, AND HITCHIN CONNECTIONS

Published online by Cambridge University Press:  18 April 2006

ZIV RAN
ZIV RAN
Affiliation:
Mathematics Department, University of California, Riverside, CA 92521, USAziv@math.ucr.edu
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Abstract

We develop some cohomological tools for the study of the local geometry of moduli and parameter spaces in complex Algebraic Geometry. Notably, we develop canonical formulae for the differential operators of arbitrary order and their natural action on suitable `natural' modules (for example, functions); in particular, we obtain a formula, in terms of the moduli problem, for the Lie bracket of vector fields on a moduli space. As an application, we obtain another construction and proof of flatness for the familiar KZW or Hitchin connection on moduli spaces of curves.

Keywords

14D1532G05
Type
Research Article
Information
Proceedings of the London Mathematical Society , Volume 92 , Issue 3 , May 2006 , pp. 545 - 580
Copyright
2006 London Mathematical Society

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Footnotes

Research partially supported by NSA Grants MDA904-02-1-0094 and H98230-05-1-0063.