An Exponential Rarefaction Result for Sub-Gaussian Real Algebraic Maximal Curves
Algebraic Geometry
2025-04-30 v3 Complex Variables
Probability
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.
Keywords
Cite
@article{arxiv.2212.02343,
title = {An Exponential Rarefaction Result for Sub-Gaussian Real Algebraic Maximal Curves},
author = {Turgay Bayraktar and Emel Karaca},
journal= {arXiv preprint arXiv:2212.02343},
year = {2025}
}
Comments
Minor revisions. To appear in Comptes Rendus Math\'ematique