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Proceedings of the American Mathematical Society

Published by the American Mathematical Society, the Proceedings of the American Mathematical Society (PROC) is devoted to research articles of the highest quality in all areas of pure and applied mathematics.

ISSN 1088-6826 (online) ISSN 0002-9939 (print)

The 2020 MCQ for Proceedings of the American Mathematical Society is 0.85.

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Realization of an equivariant holomorphic Hermitian line bundle as a Quillen determinant bundle
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by Indranil Biswas PDF
Proc. Amer. Math. Soc. 143 (2015), 3183-3187 Request permission

Abstract:

Let $M$ be an irreducible smooth complex projective variety equipped with an action of a compact Lie group $G$, and let $({\mathcal L} ,h)$ be a $G$–equivariant holomorphic Hermitian line bundle on $M$. Given a compact connected Riemann surface $X$, we construct a $G$–equivariant holomorphic Hermitian line bundle $(L ,H)$ on $X\times M$ (the action of $G$ on $X$ is trivial) such that the corresponding Quillen determinant line bundle $({\mathcal Q} , h_Q)$, which is a $G$–equivariant holomorphic Hermitian line bundle on $M$, is isomorphic to the given $G$–equivariant holomorphic Hermitian line bundle $({\mathcal L} ,h)$. This proves a conjecture by Dey and Mathai (2013).
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Additional Information
  • Indranil Biswas
  • Affiliation: School of Mathematics, Tata Institute of Fundamental Research, Homi Bhabha Road, Bombay 400005, India
  • MR Author ID: 340073
  • Email: indranil@math.tifr.res.in
  • Received by editor(s): March 10, 2014
  • Published electronically: February 5, 2015
  • Communicated by: Varghese Mathai
  • © Copyright 2015 American Mathematical Society
  • Journal: Proc. Amer. Math. Soc. 143 (2015), 3183-3187
  • MSC (2010): Primary 58J52, 14H60
  • DOI: https://doi.org/10.1090/S0002-9939-2015-12512-9
  • MathSciNet review: 3336643