2013 Fiscal Year Final Research Report
Stability conditions on triangulated categories and counting invariants
| Project/Area Number |
22684002
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| Research Category |
Grant-in-Aid for Young Scientists (A)
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| Allocation Type | Single-year Grants |
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| Research Field |
Algebra
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| Research Institution | The University of Tokyo |
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Principal Investigator |
TODA Yukinobu 東京大学, カブリ数物連携宇宙研究機構, 特任准教授 (20503882)
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| Project Period (FY) |
2010-04-01 – 2014-03-31
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| Keywords | 連接層の導来圏 / 安定性条件 / Donaldson-Thomas不変量 |
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| Research Abstract |
A 3-dimensional Calabi-Yau manifold is expected to appear as an extra dimension in string theory, and an important space both in mathematics and physics. The Donaldson-Thomas (DT) invariants counting curves on that space are conjectured to satisfy several properties originating with string theory. I constructed invariants counting semistable objects in derived categories of coherent sheaves, and applied them for several conjectures on DT invariants.
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