Holomorphic Quillen determinant line bundles on integral compact Kähler manifolds

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.