Tau-functions on spaces of abelian differentials and higher genus generalizations of ray-singer formula

Aleksey Kokotov Concordia University Dmitry Korotkin Concordia University

Differential Geometry mathscidoc:1609.10112

Journal of Differential Geometry, 82, (1), 35-100, 2009
Let w be an Abelian differential on a compact Riemann surface of genus g ≥ 1. Then |w|2 defines a flat metric with conical singularities and trivial holonomy on the Riemann surface. We obtain an explicit holomorphic factorization formula for the ζ-regularized determinant of the Laplacian in the metric |w|2, generalizing the classical Ray-Singer result in g = 1.
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@inproceedings{aleksey2009tau-functions,
  title={TAU-FUNCTIONS ON SPACES OF ABELIAN DIFFERENTIALS AND HIGHER GENUS GENERALIZATIONS OF RAY-SINGER FORMULA},
  author={Aleksey Kokotov, and Dmitry Korotkin},
  url={http://archive.ymsc.tsinghua.edu.cn/pacm_paperurl/20160911182410157030769},
  booktitle={Journal of Differential Geometry},
  volume={82},
  number={1},
  pages={35-100},
  year={2009},
}
Aleksey Kokotov, and Dmitry Korotkin. TAU-FUNCTIONS ON SPACES OF ABELIAN DIFFERENTIALS AND HIGHER GENUS GENERALIZATIONS OF RAY-SINGER FORMULA. 2009. Vol. 82. In Journal of Differential Geometry. pp.35-100. http://archive.ymsc.tsinghua.edu.cn/pacm_paperurl/20160911182410157030769.
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