| Budget Amount *help |
¥4,420,000 (Direct Cost: ¥3,400,000、Indirect Cost: ¥1,020,000)
Fiscal Year 2021: ¥1,300,000 (Direct Cost: ¥1,000,000、Indirect Cost: ¥300,000)
Fiscal Year 2020: ¥1,040,000 (Direct Cost: ¥800,000、Indirect Cost: ¥240,000)
Fiscal Year 2019: ¥1,040,000 (Direct Cost: ¥800,000、Indirect Cost: ¥240,000)
Fiscal Year 2018: ¥1,040,000 (Direct Cost: ¥800,000、Indirect Cost: ¥240,000)
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| Outline of Final Research Achievements |
We constructed a Morse homotopy category of the moment polytope in the case of the projective spaces, products of them and degree 1 Hirzebruch surface and gave a concrete description of the mirror functor from the DG category of holomorphic line bundles to the Morse homotopy category (joint work with Hiroshige Kajiura). This is a version of homotogical mirror symmetry based on the SYZ fibration.
We also defined an equivariant Fukaya category of the 1 dimensional projective space and 1 dimensional complex plane and saw that the curvature term recovers Givental's equivariant Landau-Ginzburg potential, and proved a version of equivariant homological mirror symmetry. We also found a new phenomenon which does not occur in the non-equivariant case (joint work with Fumihiko Sanda).
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