Tohoku Mathematical Journal

Canonical filtrations and stability of direct images by Frobenius morphisms

Yukinori Kitadai and Hideyasu Sumihiro

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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 $K_X$.

Article information

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

Dates
First available in Project Euclid: 7 July 2008

Permanent link to this document
https://projecteuclid.org/euclid.tmj/1215442876

Digital Object Identifier
doi:10.2748/tmj/1215442876

Mathematical Reviews number (MathSciNet)
MR2428865

Zentralblatt MATH identifier
1201.14030

Subjects
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

Keywords
Vector bundles stability Frobenius morphisms canonical filtrations geography

Citation

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. https://projecteuclid.org/euclid.tmj/1215442876


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