What is the total Betti number of a random real hypersurface?
Résumé
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 Hörmander's theory of peak sections as well as the formula of Poincaré-Martinelli.
Domaines
Géométrie algébrique [math.AG]
Origine : Fichiers produits par l'(les) auteur(s)