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

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

2011-03-23

arxiv.org/abs/1103.4598v1

Mathematics

Complex Variables

14 pages

Scientific paper

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\"{a}hler manifold $(M,\omega)$. We then prove that the critical radius of the Kodaira embedding $\Phi_N:M\rightarrow \CP^n$ given by an orthonormal basis of $H^0(M,L^N)$ is bounded below when $N\rightarrow \infty$. This result also gives conditions about when the preceding formula is valid.

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