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arXiv · 1202.5213

Holomorphic Quillen determinant line bundles on integral compact Kahler manifolds

Rukmini Dey·Varghese Mathai
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Abstract

We show that any compact Kahler manifold with integral Kahler form, parametrizes a natural holomorphic family of Cauchy-Riemann operators on the Riemann sphere such that the Quillen determinant line bundle of this family is isomorphic to a sufficiently high tensor power of the holomorphic line bundle determined by the integral Kahler form. We also establish a symplectic version of the result. We conjecture that an equivariant version of our result is true.

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BibTeXRIS

Rukmini Dey, Varghese Mathai. 2012-02-23. Holomorphic Quillen determinant line bundles on integral compact Kahler manifolds. https://doi.org/10.1093/qmath/has040

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