We show that any compact Kahler manifold with integral Kahler form,View original: http://arxiv.org/abs/1202.5213
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.