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 -