article

Title: Expected Euler characteristic of excursion sets of random holomorphic sections on complex manifolds

Authors: Jingzhou Sun

Issue: Volume 61 (2012), Issue 3, 1157-1174

Abstract:

$We prove a formula for the expected Euler characteristic of excursion sets of random sections of powers of an ample bundle $(L,h)$, where $h$ is a Hermitian metric, over a K\"ahler manifold $(M,\omega)$. We then prove that the critical radius of the Kodaira embedding $\Phi_N:M\to\mathbb{C}\mathbb{P}^n$ given by an orthonormal basis of $H^0(M,L^N)$ is bounded below when $N\to\infty$. This result also gives conditions about when the preceding formula is valid.$