[Remarques sur les courbes rationnelles minimales sur les espaces des modules de faisceaux stables]
Soient C une courbe projective lisse de genre et M l'espace des modules de faisceaux stables de rang 2 et de déterminant fixe de degré d sur C. Nous prouvons que, lorsque et d est pair, il existe, pour tout point , une courbe rationnelle minimale passant par , qui n'est pas une courbe de Hecke. Cela complète un théorème de Xiaotao Sun.
Let C be a smooth projective curve of genus over an algebraically closed field of characteristic zero, and M be the moduli space of stable bundles of rank 2 and with fixed determinant of degree d on the curve C. When and d is even, we prove that, for any point , there is a minimal rational curve passing through , which is not a Hecke curve. This complements a theorem of Xiaotao Sun.
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@article{CRMATH_2016__354_10_1013_0,
author = {Liu, Min},
title = {Remarks on minimal rational curves on moduli spaces of stable bundles},
journal = {Comptes Rendus. Math\'ematique},
pages = {1013--1017},
publisher = {Elsevier},
volume = {354},
number = {10},
year = {2016},
doi = {10.1016/j.crma.2016.08.007},
language = {en},
url = {http://www.numdam.org/articles/10.1016/j.crma.2016.08.007/}
}
TY - JOUR AU - Liu, Min TI - Remarks on minimal rational curves on moduli spaces of stable bundles JO - Comptes Rendus. Mathématique PY - 2016 SP - 1013 EP - 1017 VL - 354 IS - 10 PB - Elsevier UR - http://www.numdam.org/articles/10.1016/j.crma.2016.08.007/ DO - 10.1016/j.crma.2016.08.007 LA - en ID - CRMATH_2016__354_10_1013_0 ER -
%0 Journal Article %A Liu, Min %T Remarks on minimal rational curves on moduli spaces of stable bundles %J Comptes Rendus. Mathématique %D 2016 %P 1013-1017 %V 354 %N 10 %I Elsevier %U http://www.numdam.org/articles/10.1016/j.crma.2016.08.007/ %R 10.1016/j.crma.2016.08.007 %G en %F CRMATH_2016__354_10_1013_0
Liu, Min. Remarks on minimal rational curves on moduli spaces of stable bundles. Comptes Rendus. Mathématique, Tome 354 (2016) no. 10, pp. 1013-1017. doi : 10.1016/j.crma.2016.08.007. http://www.numdam.org/articles/10.1016/j.crma.2016.08.007/
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☆ Supported by the National Natural Science Foundation of China (Grant No. 11401330).
