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July 2008 Canonical filtrations and stability of direct images by Frobenius morphisms II
Yukinori Kitadai, Hideyasu Sumihiro
Hiroshima Math. J. 38(2): 243-261 (July 2008). DOI: 10.32917/hmj/1220619460


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.


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Yukinori Kitadai. Hideyasu Sumihiro. "Canonical filtrations and stability of direct images by Frobenius morphisms II." Hiroshima Math. J. 38 (2) 243 - 261, July 2008.


Published: July 2008
First available in Project Euclid: 5 September 2008

zbMATH: 1201.14030
MathSciNet: MR2428865
Digital Object Identifier: 10.32917/hmj/1220619460

Primary: 14J60
Secondary: 13A35, 14J29

Rights: Copyright © 2008 Hiroshima University, Mathematics Program


Vol.38 • No. 2 • July 2008
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