Gromov-Witten theory and mirror symmetry
| Project/Area Number |
22740042
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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 |
Geometry
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| Research Institution | Kyoto University |
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Principal Investigator |
IRITANI Hiroshi 京都大学, 大学院・理学研究科, 准教授 (20448400)
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| Project Period (FY) |
2010 – 2012
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| Project Status |
Completed (Fiscal Year 2012)
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| Budget Amount *help |
¥4,160,000 (Direct Cost: ¥3,200,000、Indirect Cost: ¥960,000)
Fiscal Year 2012: ¥1,300,000 (Direct Cost: ¥1,000,000、Indirect Cost: ¥300,000)
Fiscal Year 2011: ¥1,300,000 (Direct Cost: ¥1,000,000、Indirect Cost: ¥300,000)
Fiscal Year 2010: ¥1,560,000 (Direct Cost: ¥1,200,000、Indirect Cost: ¥360,000)
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| Keywords | ミラー対称性 / グロモフ・ウィッテン理論 / トーリック多様体 / 量子コホモロジー / ホッジ理論 / 軌道体 / 幾何学的量子化 / Seidel表現 / Gromov-Witten理論 / Seidel 元 / 量子化 / 収束 / Giventalの公式 / Gromov-Witten不変量 / Gromov-Wittenポテンシャル / 量子コホモロモジー / カラビ・ヤウ多様体 / FJRW理論 / Seidel元 / カラビ・ヤウ超曲面 |
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| Research Abstract |
We studied a global structure of Gromov-Witten theory from a viewpoint of mirror symmetry. Our results include:
(1) mirror symmetry for complete intersections in toric orbifold and matching of integral structures from the A-model andthe B-model
(2) Landau-Ginzburg/Calabi-Yau correspondence for weighted projective Calabi-Yau hypersurfaces and its relation to Orlov’s derived equivalence
(3) Seidel representation for toric manifolds and the relation to mirror transformation.
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Report
(4 results)
Research Products
(29 results)
