Sun, Jingzhou Expected Euler characteristic of excursion sets of random holomorphic sections on complex manifolds. (English) Zbl 1271.32031 Indiana Univ. Math. J. 61, No. 3, 1157-1174 (2012). Summary: 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 Kähler 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. Cited in 4 Documents MSC: 32Q99 Complex manifolds Keywords:excursion sets of random sections; expected Euler characteristic; critical radius of the Kodaira embedding PDFBibTeX XMLCite \textit{J. Sun}, Indiana Univ. Math. J. 61, No. 3, 1157--1174 (2012; Zbl 1271.32031) Full Text: DOI arXiv Link