2010 Fiscal Year Final Research Report
A study on adjoint ideal sheaves by characteristic p methods
| Project/Area Number |
20740019
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| Research Category |
Grant-in-Aid for Young Scientists (B)
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| Allocation Type | Single-year Grants |
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| Research Field |
Algebra
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| Research Institution | Kyushu University |
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Principal Investigator |
TAKAGI Shunsuke Kyushu University, 大学院・数理学研究院, 特任准教授 (40380670)
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| Project Period (FY) |
2008 – 2010
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| Keywords | 代数幾何 / 可換環論 / 特異点論 |
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| Research Abstract |
We introduced the notions of adjoint ideal sheaves and maximal non-lc ideal sheaves as analogs or variants of multiplier ideal sheaves, and then we studied their local properties by characteristic pmethods such as tight closure and Frobenius splitting. Also, we carried out a systematic study of invariants (F-jumping numbers, parameter F-jumping number, F-thresholds and non-F-pure ideals) related to test ideals, which can be viewed as a positive characteristic analog of multiplier ideal sheaves.
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