TY - JOUR

T1 - A local families index formula for ∂-operators on punctured riemann surfaces

AU - Albin, Pierre

AU - Rochon, Frédéric

N1 - Funding Information:
The second author was supported by a postdoctoral fellowship of the Fonds québécois de la recherche sur la nature et les technologies.
Funding Information:
The first author was partially supported by a NSF postdoctoral fellowship.

PY - 2009/7

Y1 - 2009/7

N2 - Using heat kernel methods developed by Vaillant, a local index formula is obtained for families of ∂-operators on the Teichmüller universal curve of Riemann surfaces of genus g with n punctures. The formula also holds on the moduli space Mg,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.

AB - Using heat kernel methods developed by Vaillant, a local index formula is obtained for families of ∂-operators on the Teichmüller universal curve of Riemann surfaces of genus g with n punctures. The formula also holds on the moduli space Mg,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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U2 - 10.1007/s00220-009-0816-2

DO - 10.1007/s00220-009-0816-2

M3 - Article

AN - SCOPUS:67349151781

SN - 0010-3616

VL - 289

SP - 483

EP - 527

JO - Communications in Mathematical Physics

JF - Communications in Mathematical Physics

IS - 2

ER -