Holomorphic 𝐿² torsion without determinant class condition

Su, Guangxiang

doi:10.1090/S0002-9939-2015-12565-8

Holomorphic $L^2$ torsion without determinant class condition
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by Guangxiang Su

Proc. Amer. Math. Soc. 143 (2015), 4513-4524

DOI: https://doi.org/10.1090/S0002-9939-2015-12565-8

Published electronically: March 17, 2015

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Abstract:

In this paper, we extend the holomorphic $L^{2}$ torsion introduced by Carey, Farber and Mathai to the case without the determinant class condition. We compute the metric variation formula for the holomorphic $L^{2}$ torsion in our case. We also study the asymptotics of the holomorphic $L^{2}$ torsion associated with a power of a positive line bundle.

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