What is the total Betti number of a random real hypersurface
What is the total Betti number of a random real hypersurface
复制标题
随机实超曲面的总贝蒂数是多少
DOI：
10.1515/crelle-2012-0062
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发表时间：
2011
期刊：
影响因子：
--
通讯作者：
Jean
中科院分区：
文献类型：
--
作者：
D. Gayet;Jean
本文从光滑真实的射影流形上的高次随机真实的超曲面的期望总Betti数的上界出发，得到了该超曲面的期望总Betti数.这个上界是从限制在这样一个随机超曲面的复域上的真实的Lefschetz束的临界点的等距划分推导出来的，等距划分是我们首先建立的。我们的证明涉及到H“Ormander的峰截面理论以及Poincar 'e-Martinelli的公式。
We bound from above the expected total Betti number of a high degree random real hypersurface in a smooth real projective manifold. This upper bound is deduced from the equirepartition of critical points of a real Lefschetz pencil restricted to the complex domain of such a random hypersurface, equirepartition which we first establish. Our proofs involve H\"ormander's theory of peak sections as well as the formula of Poincar\'e-Martinelli.