Exponential rarefaction of real curves with many components
Gayet, Damien1 ; Welschinger, Jean-Yves1
1 CNRS UMR 5208, Université Lyon 1, Institut Camille Jordan, Université de Lyon 69622, Villeurbanne Cedex France
Publications Mathématiques de l'IHÉS, Tome 113 (2011), pp. 69-96.

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 d∈ℕ∗ 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.

DOI : 10.1007/s10240-011-0033-3
Gayet, Damien 1 ; Welschinger, Jean-Yves 1

1 CNRS UMR 5208, Université Lyon 1, Institut Camille Jordan, Université de Lyon 69622, Villeurbanne Cedex France 
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Gayet, Damien; Welschinger, Jean-Yves. Exponential rarefaction of real curves with many components. Publications Mathématiques de l'IHÉS, Tome 113 (2011), pp. 69-96. doi : 10.1007/s10240-011-0033-3. http://www.numdam.org/articles/10.1007/s10240-011-0033-3/

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