Omega Admissible Theory II: New metrics on determinant of cohomology And Their applications to moduli spaces of punctured Riemann surfaces

Details Omega Admissible Theory II: New metrics on determinant of cohomology And Their applications to moduli spaces of punctured Riemann surfaces Omega Admissible Theory II: New metrics on determinant of cohomology And Their applications to moduli spaces of punctured Riemann surfaces

1998-10-19

arxiv.org/abs/math/9810116v1

Mathematics

Algebraic Geometry

AMS-TEX

Scientific paper

For singular metrics, there is no Quillen metric formalism on cohomology determinant. In this paper, we develop an admissible theory, with which the arithmetic Deligne-Riemann-Roch isometry can be established for singular metrics. As an application, we first study Weil-Petersson metrics and Takhtajan-Zograf metrics on moduli spaces of punctured Riemann surfaces, and then give a more geometric interpretation of our determinant metrics in terms of Selberg zeta functions. We end this paper by proposing an arithmetic factorization for Weil-Petersson metrics, cuspidal metrics and Selberg zeta functions.

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