Exponential rarefaction of real curves with many components |
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Authors: | Damien Gayet Jean-Yves Welschinger |
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Institution: | 1.CNRS UMR 5208, Université Lyon 1, Institut Camille Jordan,Université de Lyon,Villeurbanne Cedex,France |
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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 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. |
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Keywords: | |
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