2014/09/19 by Jean-Yves Welschinger, Welschinger, Jean-Yves
Mathematics · #14P25 #60D05 #Algebraic Geometry (math.AG) #Algebraic Geometry and Number Theory #FOS: Mathematics #Geometric Analysis and Curvature Flows #Geometry and complex manifolds #Probability (math.PR)
paper · pdf · doi:10.48550/arxiv.1409.5679
openalex publication_date 2014/09/19 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
These are notes of the mini-course I gave during the CIMPA summer school at Villa de Leyva, Colombia, in July 2014. The subject was my joint work with Damien Gayet on the topology of random real hypersurfaces, restricting myself to the case of projective spaces and focusing on our lower estimates. Namely, we estimate from (above and) below the mathematical expectation of all Betti numbers of degree d random real projective hypersurfaces. For any closed connected hypersurface Σ of ℝn, we actually estimate from below the mathematical expectation of the number of connected components of these degree d random real projective hypersurfaces which are diffeomorphic to Σ.