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arXiv · 0801.2127

A local families index formula for d-bar operators on punctured Riemann surfaces

Pierre Albin·Frederic Rochon
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Abstract

Using heat kernel methods developed by Vaillant, a local index formula is obtained for families of d-bar operators on the Teichmuller universal curve of Riemann surfaces of genus g with n punctures. The formula also holds on the moduli space M{g,n} in the sense of orbifolds where it can be written in terms of Mumford-Morita-Miller classes. The degree two part of the formula gives the curvature of the corresponding determinant line bundle equipped with the Quillen connection, a result originally obtained by Takhtajan and Zograf.

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Pierre Albin, Frederic Rochon. 2009-09-04. A local families index formula for d-bar operators on punctured Riemann surfaces. https://doi.org/10.1007/s00220-009-0816-2

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