An Exponential Rarefaction Result for Sub-Gaussian Real Algebraic Maximal Curves

Abstract

We prove that maximal real algebraic curves associated with sub-Gaussian random real holomorphic sections of a smoothly curved ample line bundle are exponentially rare. This generalizes the result of Gayet and Welschinger \cite{GW} proved in the Gaussian case for positively curved real holomorphic line bundles.

Minor revisions. To appear in Comptes Rendus Mathématique

References in corpus (3)

• Expected number of real roots for random linear combinations of orthogonal polynomials associated with radial weights
• Mass equidistribution for random polynomials
• Exponential rarefaction of maximal real algebraic hypersurfaces