Canonical filtrations and stability of direct images by Frobenius morphisms

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概要

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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 $K_X$.

• 東北大学の論文
• 2008-06-00

著者

• Sumihiro Hideyasu

  Department of Mathematics Graduate School of Science Hiroshima University Higashi-Hiroshima 739-8526 Japan

• Kitadai Yukinori

  Department of Mathematics, Graduate School of Science, Hiroshima University

• SUMIHIRO Hideyasu

  DEPARTMENT OF MATHEMATICS FACULTY OF SCIENCE HIROSHIMA UHIVERSITY

• Kitadai Yukinori

  Department of Mathematics Graduate School of Science Hiroshima University Higashi-Hiroshima 739-8526 Japan

関連論文

• A splitting theorem for rank two vector bundles on projective spaces in positive characteristic
• Canonical filtrations and stability of direct images by Frobenius morphisms
• Canonical filtrations and stability of direct images by Frobenius morphisms II
• Determinantal varieties associated to rank two vector bundles on projective spaces and splitting theorems

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