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arXiv · 1107.2288

What is the total Betti number of a random real hypersurface?

Damien Gayet·Jean-Yves Welschinger
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Abstract

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.

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Damien Gayet, Jean-Yves Welschinger. 2011-07-12. What is the total Betti number of a random real hypersurface?. https://arxiv.org/abs/1107.2288

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