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2008 Canonical filtrations and stability of direct images by Frobenius morphisms
Yukinori Kitadai, Hideyasu Sumihiro
Tohoku Math. J. (2) 60(2): 287-301 (2008). DOI: 10.2748/tmj/1215442876

Abstract

We study the stability of direct images by Frobenius morphisms. First, we compute the first Chern classes of direct images of vector bundles by Frobenius morphisms modulo rational equivalence up to torsions. Next, introducing the canonical filtrations, we prove that if $X$ is a nonsingular projective minimal surface of general type with semistable $\Omega_X^1$ with respect to the canonical line bundle $K_X$, then the direct images of line bundles on $X$ by Frobenius morphisms are semistable with respect to $K_X$.

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Yukinori Kitadai. Hideyasu Sumihiro. "Canonical filtrations and stability of direct images by Frobenius morphisms." Tohoku Math. J. (2) 60 (2) 287 - 301, 2008. https://doi.org/10.2748/tmj/1215442876

Information

Published: 2008
First available in Project Euclid: 7 July 2008

zbMATH: 1201.14030
MathSciNet: MR2428865
Digital Object Identifier: 10.2748/tmj/1215442876

Subjects:
Primary: 14J60
Secondary: 13A35, 14J29

Rights: Copyright © 2008 Tohoku University

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Vol.60 • No. 2 • 2008
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