Tohoku Mathematical Journal

Canonical filtrations and stability of direct images by Frobenius morphisms

Yukinori Kitadai and Hideyasu Sumihiro

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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 $K_X$.

Article information

Tohoku Math. J. (2), Volume 60, Number 2 (2008), 287-301.

First available in Project Euclid: 7 July 2008

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Zentralblatt MATH identifier

Primary: 14J60: Vector bundles on surfaces and higher-dimensional varieties, and their moduli [See also 14D20, 14F05, 32Lxx]
Secondary: 13A35: Characteristic p methods (Frobenius endomorphism) and reduction to characteristic p; tight closure [See also 13B22] 14J29: Surfaces of general type

Vector bundles stability Frobenius morphisms canonical filtrations geography


Kitadai, Yukinori; Sumihiro, Hideyasu. Canonical filtrations and stability of direct images by Frobenius morphisms. Tohoku Math. J. (2) 60 (2008), no. 2, 287--301. doi:10.2748/tmj/1215442876.

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