| Project/Area Number |
23540068
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| Research Category |
Grant-in-Aid for Scientific Research (C)
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| Allocation Type | Multi-year Fund |
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| Section | 一般 |
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| Research Field |
Geometry
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| Research Institution | Yamagata University |
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Principal Investigator |
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| Co-Investigator(Renkei-kenkyūsha) |
TOMARU Tadashi 群馬大学, 医学部, 教授 (70132579)
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| Project Period (FY) |
2011 – 2013
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| Project Status |
Completed (Fiscal Year 2013)
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| Budget Amount *help |
¥3,510,000 (Direct Cost: ¥2,700,000、Indirect Cost: ¥810,000)
Fiscal Year 2013: ¥1,040,000 (Direct Cost: ¥800,000、Indirect Cost: ¥240,000)
Fiscal Year 2012: ¥1,040,000 (Direct Cost: ¥800,000、Indirect Cost: ¥240,000)
Fiscal Year 2011: ¥1,430,000 (Direct Cost: ¥1,100,000、Indirect Cost: ¥330,000)
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| Keywords | 2次元特異点 / 幾何種数 / 擬斉次特異点 / 2次元正規特異点 / good ideal / ２次元特異点 |
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| Research Abstract |
We studied fundamental analytic invariants of complex normal surface singularities, such as geometric genus. For a weighted homogeneous singularity with rational homology sphere link, we expressed the dimension of the first cohomology group of the tangent sheaf on the minimal good resolution using Seifert invariants (joint work with A. Nemethi). We introduced a notion of pg-cycle and investigated fundamental properties, and then for Gorenstein singularities and rational singularities, we proved that the good ideal exists, and furthermore that good ideals for rational singularities correspond to nef cycles on the minimal resolution (joint work with Kei-ichi Watanabe and Ken-ichi Yoshida). We also gave an explicit expression of the maximal ideal cycle on a complete intersection of Brieskorn type (joint work with Fan-Ning Meng). This generalizes the results by Konno and Nagashima for Brieskorn hypersurfaces.
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