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arXiv · 1005.3228

Exponential rarefaction of real curves with many components

Damien Gayet·Jean-Yves Welschinger
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Abstract

Given a positive real Hermitian holomorphic line bundle L over a smooth real projective manifold X, the space of real holomorphic sections of the bundle L^d inherits for every positive integer d a L^2 scalar product which induces a Gaussian measure. When X is a curve or a surface, we estimate the volume of the cone of real sections whose vanishing locus contains many real components. In particular, the volume of the cone of maximal real sections decreases exponentially as d grows to infinity.

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Damien Gayet, Jean-Yves Welschinger. 2010-05-18. Exponential rarefaction of real curves with many components. https://arxiv.org/abs/1005.3228

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