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Holomorphic $ L^2$ torsion without determinant class condition

Author: Guangxiang Su
Journal: Proc. Amer. Math. Soc. 143 (2015), 4513-4524
MSC (2010): Primary 58J52
Published electronically: March 17, 2015
MathSciNet review: 3373949
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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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Guangxiang Su
Affiliation: Chern Institute of Mathematics and LPMC, Nankai University, Tianjin 300071, People’s Republic of China

Keywords: Holomorphic $L^2$ torsion, determinant class condition, positive line bundle
Received by editor(s): June 6, 2014
Received by editor(s) in revised form: June 12, 2014
Published electronically: March 17, 2015
Additional Notes: The author was supported by “the Fundamental Research Funds for the Central Universities 65011541” and NSFC 11101219
Communicated by: Varghese Mathai
Article copyright: © Copyright 2015 American Mathematical Society