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

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

2008-01-14

arxiv.org/abs/0801.2127v2

Comm. Math. Phys. 289 (2009), no.2, 483-527

Mathematics

Differential Geometry

47 pages

Scientific paper

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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