Tohoku Mathematical Journal
- Tohoku Math. J. (2)
- Volume 60, Number 2 (2008), 287-301.
Canonical filtrations and stability of direct images by Frobenius morphisms
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 $K_X$.
Tohoku Math. J. (2), Volume 60, Number 2 (2008), 287-301.
First available in Project Euclid: 7 July 2008
Permanent link to this document
Digital Object Identifier
Mathematical Reviews number (MathSciNet)
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
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