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Realization of an equivariant holomorphic Hermitian line bundle as a Quillen determinant bundle


Author: Indranil Biswas
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
Published electronically: February 5, 2015
MathSciNet review: 3336643
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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).


References [Enhancements On Off] (What's this?)

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Additional Information

Indranil Biswas
Affiliation: School of Mathematics, Tata Institute of Fundamental Research, Homi Bhabha Road, Bombay 400005, India
Email: indranil@math.tifr.res.in

DOI: https://doi.org/10.1090/S0002-9939-2015-12512-9
Keywords: Quillen determinant, equivariant bundle, fiber integral
Received by editor(s): March 10, 2014
Published electronically: February 5, 2015
Communicated by: Varghese Mathai
Article copyright: © Copyright 2015 American Mathematical Society

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