Tohoku Mathematical Journal
2008
June
SECOND SERIES VOL. 60, NO. 2

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

Title CANONICAL FILTRATIONS AND STABILITY OF DIRECT IMAGES BY FROBENIUS MORPHISMS

Author Yukinori Kitadai and Hideyasu Sumihiro

(Received December 12, 2006, revised October 17, 2007)
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 $K_X$.

2000 Mathematics Subject Classification. Primary 14J60; Secondary 13A35, 14J29.
Key words and phrases. Vector bundles, stability, Frobenius morphisms, canonical filtrations, geography.

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