1 results
Bergman metrics and geodesics in the space of Kähler metrics on principally polarized abelian varieties
- Part of
-
- Journal:
- Journal of the Institute of Mathematics of Jussieu / Volume 11 / Issue 1 / January 2012
- Published online by Cambridge University Press:
- 21 June 2011, pp. 1-25
- Print publication:
- January 2012
-
- Article
- Export citation
-
It is well known in Kähler geometry that the infinite-dimensional symmetric space
of smooth Kähler metrics in a fixed Kähler class on a polarized Kähler manifold is well approximated by finite-dimensional submanifolds 
of Bergman metrics of height k. Then it is natural to ask whether geodesics in can be approximated by Bergman geodesics in 
. For any polarized Kähler manifold, the approximation is in the C0 topology. For some special varieties, one expects better convergence: Song and Zelditch proved the C2 convergence for the torus-invariant metrics over toric varieties. In this article, we show that some C∞ approximation exists as well as a complete asymptotic expansion for principally polarized abelian varieties.
of smooth Kähler metrics in a fixed Kähler class on a polarized Kähler manifold is well approximated by finite-dimensional submanifolds 
of Bergman metrics of height 
. For any polarized Kähler manifold, the approximation is in the 