Research on generalized geometric structures, 4 dimensional differential topology and derived category
| Project/Area Number |
25610011
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| Research Category |
Grant-in-Aid for Challenging Exploratory Research
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| Allocation Type | Multi-year Fund |
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| Research Field |
Geometry
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| Research Institution | Osaka University |
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Principal Investigator |
Goto Ryushi 大阪大学, 理学(系)研究科(研究院), 教授 (30252571)
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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 |
¥3,900,000 (Direct Cost: ¥3,000,000、Indirect Cost: ¥900,000)
Fiscal Year 2015: ¥1,170,000 (Direct Cost: ¥900,000、Indirect Cost: ¥270,000)
Fiscal Year 2014: ¥1,170,000 (Direct Cost: ¥900,000、Indirect Cost: ¥270,000)
Fiscal Year 2013: ¥1,560,000 (Direct Cost: ¥1,200,000、Indirect Cost: ¥360,000)
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| Keywords | 一般化された複素構造 / 一般化されたケーラー構造 / ポアソン構造 / 変形理論 / モジュライ空間 / flat structure / 非可換代数幾何 / 導来圏の変形 / 非可換曲面 / ツイスター空間 / ４次元多様体 / 一般化されたカラビーヤオ構造 / 超ケーラー多様体 |
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| Outline of Final Research Achievements |
The author's results are mainly as follows. (1) We show that generalized complex structures on a complex surface induced from a holomorphic Poisson structure admit unobstructed deformations, i.e., the Kuranishi spaces are smooth. We construct moduli spaces of generalized complex structures induced from Poisson structures on del Pezzo surfaces. Further it turns out that the moduli space admits "Stratified flat structure", that is, the moduli space has a stratification which is constructed from the types of singularities of jumping locus and each strata admits a flat structure, i.e., a torsion free flat connection of the tangent bundle. (2) We obtain a new family of generalized complex structures with k connected components of jumping loci for any k on certain 4-manifolds which have neither complex structures and symplectic structures, by using logarithmic transformation of multiplicity m. These two results are already written in our paper [1] , [2] and they are accepted for publication.
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Report
(4 results)
Research Products
(21 results)
