2009 Fiscal Year Final Research Report
Stability of direct images by Frobenius morphisms and algebraic geometry in positive characteristic
| Project/Area Number |
20840032
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| Research Category |
Grant-in-Aid for Young Scientists (Start-up)
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| Allocation Type | Single-year Grants |
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| Research Field |
Algebra
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| Research Institution | Hiroshima University |
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Principal Investigator |
KITADAI Yukinori Hiroshima University, 工学研究科, 特任助教 (30511563)
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| Project Period (FY) |
2008 – 2009
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| Keywords | ベクトル束 / 安定性 / 半安定ベクトル束 / 正標数 / フロベニウス写像 / de Rham複体 / 小平消滅定理 |
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| Research Abstract |
We studied the problem of whether taking direct images of semistable vector bundles on algebraic varieties in positive characteristic by Frobenius morphisms preserves semistability or not and related problems. Calculations to find concrete examples of algebraic surfaces whose cotangent bundles are semitable or are not semistable by Frobenius pullback several times were proceeded.
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