What is the total Betti number of a random real hypersurface?
Algebraic Geometry
2011-07-13 v1
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.
Keywords
Cite
@article{arxiv.1107.2288,
title = {What is the total Betti number of a random real hypersurface?},
author = {Damien Gayet and Jean-Yves Welschinger},
journal= {arXiv preprint arXiv:1107.2288},
year = {2011}
}