Behavior of Welschinger invariants under Morse simplifications
Bernstein and van der Corput-Schaake type inequalities on semialgebraic curves
We show that in the class of compact, piecewise curves K in , the semialgebraic curves are exactly those which admit a Bernstein (or a van der Corput-Schaake) type inequality for the derivatives of (the traces of) polynomials on K.
Betti numbers of random real hypersurfaces and determinants of random symmetric matrices
We asymptotically estimate from above the expected Betti numbers of random real hypersurfaces in smooth real projective manifolds. Our upper bounds grow as the square root of the degree of the hypersurfaces as the latter grows to infinity, with a coefficient involving the Kählerian volume of the real locus of the manifold as well as the expected determinant of random real symmetric matrices of given index. In particular, for large dimensions, these coefficients get exponentially small away from...
Betti numbers of real elliptic surfaces. (Nombres de Betti des surfaces elliptiques réelles.)
Binäre Formen und Primideale.
Bounding the Number of Connected Components of a Real Algebraic Set.
Bounds for the number of connected components and the first Betti number mod two of a real algebraic surface