English

Holomorphic Quillen determinant line bundles on integral compact Kahler manifolds

Mathematical Physics 2013-09-02 v3 High Energy Physics - Theory Differential Geometry Geometric Topology math.MP Symplectic Geometry

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.

Keywords

Cite

@article{arxiv.1202.5213,
  title  = {Holomorphic Quillen determinant line bundles on integral compact Kahler manifolds},
  author = {Rukmini Dey and Varghese Mathai},
  journal= {arXiv preprint arXiv:1202.5213},
  year   = {2013}
}

Comments

Latex2e, 10 pages, To appear in, Quillen memorial issue, Quarterly J. Math