Friday, February 24, 2012

1202.5213 (Rukmini Dey et al.)

Holomorphic Quillen determinant line bundles on integral compact Kahler

Rukmini Dey, Varghese Mathai
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 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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