We study the stability of direct images by Frobenius morphisms. We prove that if the cotangent vector bundle of a nonsingular projective surface $X$ is semistable with respect to a numerically positive polarization divisor satisfying certain conditions, then the direct images of the cotangent vector bundle tensored with line bundles on $X$ by Frobenius morphisms are semistable with respect to the polarization. Hence we see that the de Rham complex of $X$ consists of semistable vector bundles if $X$ has the semistable cotangent vector bundle with respect to the polarization with certain mild conditions.
Publié le : 2008-07-15
Classification:
Vector bundles,
stability,
Frobenius morphisms,
canonical filtrations,
de Rham complexes,
Kodaira vanishing,
14J60,
13A35,
14J29
@article{1220619460,
author = {Kitadai, Yukinori and Sumihiro, Hideyasu},
title = {Canonical filtrations and stability of direct images by Frobenius morphisms II},
journal = {Hiroshima Math. J.},
volume = {38},
number = {1},
year = {2008},
pages = { 243-261},
language = {en},
url = {http://dml.mathdoc.fr/item/1220619460}
}
Kitadai, Yukinori; Sumihiro, Hideyasu. Canonical filtrations and stability of direct images by Frobenius morphisms II. Hiroshima Math. J., Tome 38 (2008) no. 1, pp. 243-261. http://gdmltest.u-ga.fr/item/1220619460/