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

Pierre Albin, Frédéric Rochon

Research output: Contribution to journalArticlepeer-review


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.

Original languageEnglish (US)
Pages (from-to)483-527
Number of pages45
JournalCommunications in Mathematical Physics
Issue number2
StatePublished - Jul 2009
Externally publishedYes

ASJC Scopus subject areas

  • Statistical and Nonlinear Physics
  • Mathematical Physics


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