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arxiv 1103.4598 v1 pith:44C6I7PI submitted 2011-03-23 math.CV math.AGmath.PR

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

classification math.CV math.AGmath.PR
keywords characteristiceulerexcursionexpectedformulaproverandomrightarrow
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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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