Canonical filtrations and stability of direct images by Frobenius morphisms II

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概要

• 論文の詳細を見る

• We study the stability of direct images by Frobenius morphisms. We prove thatif the cotangent vector bundle of a nonsingular projective surface $X$ is semistable with respect to a numerically positive polarization divisor satisfying certain conditions, then the direct images of the cotangent vector bundle tensored with line bundles on $X$ by Frobenius morphisms are semistable with respect to the polarization. Hence we see that the de Rham complex of $X$ consists of semistable vector bundles if $X$ has the semistable cotangent vector bundle with respect to the polarization with certain mild conditions.

• 広島大学の論文
• 2008-07-00

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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