Voir la notice de l'article provenant de la source Numdam
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.
Gayet, Damien 1 ; Welschinger, Jean-Yves 1
@article{PMIHES_2011__113__69_0,
author = {Gayet, Damien and Welschinger, Jean-Yves},
title = {Exponential rarefaction of real curves with many components},
journal = {Publications Math\'ematiques de l'IH\'ES},
pages = {69--96},
publisher = {Springer-Verlag},
volume = {113},
year = {2011},
doi = {10.1007/s10240-011-0033-3},
mrnumber = {2805598},
zbl = {1227.32028},
language = {en},
url = {http://geodesic.mathdoc.fr/articles/10.1007/s10240-011-0033-3/}
}
TY - JOUR AU - Gayet, Damien AU - Welschinger, Jean-Yves TI - Exponential rarefaction of real curves with many components JO - Publications Mathématiques de l'IHÉS PY - 2011 SP - 69 EP - 96 VL - 113 PB - Springer-Verlag UR - http://geodesic.mathdoc.fr/articles/10.1007/s10240-011-0033-3/ DO - 10.1007/s10240-011-0033-3 LA - en ID - PMIHES_2011__113__69_0 ER -
%0 Journal Article %A Gayet, Damien %A Welschinger, Jean-Yves %T Exponential rarefaction of real curves with many components %J Publications Mathématiques de l'IHÉS %D 2011 %P 69-96 %V 113 %I Springer-Verlag %U http://geodesic.mathdoc.fr/articles/10.1007/s10240-011-0033-3/ %R 10.1007/s10240-011-0033-3 %G en %F PMIHES_2011__113__69_0
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
Cité par Sources :