Abstract
AbstractIt is well known in Kähler geometry that the infinite-dimensional symmetric space $\mathcal{H}$ of smooth Kähler metrics in a fixed Kähler class on a polarized Kähler manifold is well approximated by finite-dimensional submanifolds $\mathcal{B}_k\subset\mathcal{H}$ of Bergman metrics of height k. Then it is natural to ask whether geodesics in $\mathcal{H}$ can be approximated by Bergman geodesics in $\mathcal{B}_k$. 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.
Publisher
Cambridge University Press (CUP)
Reference26 articles.
1. Convergence of Bergman geodesics on \mathbf{CP}^1
2. 21. Sogge C. , Fourier integrals in classical analysis, Cambridge Tracts in Mathematics (1993).
3. Almost holomorphic sections of ample line bundles over symplectic manifolds;Shiffman;J. Reine Angew. Math.,2002
4. 17. Rubinstein Y. A. , Geometric quantization and dynamical constructions on the space of Kähler metrics, PhD thesis, MIT (2008).
5. The Monge-Ampère operator and geodesics in the space of Kähler potentials
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