Deformations of real singularities and decompositions of monodromies
| Project/Area Number |
25400078
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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 | Tohoku University |
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Principal Investigator |
ISHIKAWA MASAHARU 東北大学, 理学(系)研究科(研究院), 准教授 (10361784)
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| Project Period (FY) |
2013-04-01 – 2016-03-31
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| Project Status |
Completed (Fiscal Year 2015)
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| Budget Amount *help |
¥5,070,000 (Direct Cost: ¥3,900,000、Indirect Cost: ¥1,170,000)
Fiscal Year 2015: ¥1,430,000 (Direct Cost: ¥1,100,000、Indirect Cost: ¥330,000)
Fiscal Year 2014: ¥1,430,000 (Direct Cost: ¥1,100,000、Indirect Cost: ¥330,000)
Fiscal Year 2013: ¥2,210,000 (Direct Cost: ¥1,700,000、Indirect Cost: ¥510,000)
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| Keywords | 特異点の変形 / 安定写像 / ハンドル分解 / 混合多項式 / shadow / Gromov norm |
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| Outline of Final Research Achievements |
We proved that a linear deformation of a plane curve singularity of Brieskorn type realized by adding a complex-conjugate term yields a generic map in general and estimated the number of cusps appearing after the deformation. We also proved that there exists a deformation of a real isolated singularity whose singular value set has an innermost circle with k-cusps if and only if k is not equals to 1.
On relation between stable maps and geometric structures of 3-manifolds, focusing on the correspondence between Turaev's shadows and Stein factorizations, we introduced a notion of stable map complexity by counting the number of certain singular fibers and proved that it coincides with the branched shadow complexity. Using this coincidence, we gave an estimation of hyperbolic volumes of 3-manifolds from above and below by their stable map complexities.
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Report
(4 results)
Research Products
(12 results)
