Weighted Bergman kernels on orbifolds

Toeplitz算子、次乘法滤过与加权Bergman核

Toeplitz operators, submultiplicative filtrations and weighted Bergman kernels

本文证明极化复射影流形上次乘法滤过的权重算子是Toeplitz算子，并细化加权Bergman核的渐近分析，改进跳跃测度收敛结果。

Convergence of Fubini-Study currents for orbifold line bundles

We discuss positive closed currents and Fubini-Study currents on orbifolds, as well as Bergman kernels of singular Hermitian orbifold line bundles. We prove that the Fubini-Study currents associated to high powers of a semipositive singular line bundle converge weakly to the curvature current on the set where the curvature is strictly positive, generalizing a well-known theorem of Tian. We include applications to the asymptotic distribution of zeros of random holomorphic sections.