2018 Fiscal Year Annual Research Report
Perverse sheaves of categories, and derived symmetries of 3-folds
| Project/Area Number |
16K17561
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| Research Institution | The University of Tokyo |
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Principal Investigator |
DONOVAN WILL 東京大学, カブリ数物連携宇宙研究機構, 特任研究員 (60754158)
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| Project Period (FY) |
2016-04-01 – 2019-03-31
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| Keywords | Perverse sheaves / Derived symmetries / Flops / Contractions / Variation of GIT / Mirror symmetry / Stringy Kaehler moduli |
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| Outline of Annual Research Achievements |
I constructed mirror partners for certain perverse sheaves of categories (schobers) studied earlier in the project, in collaboration with Tatsuki Kuwagaki. This resulted in joint preprint (b). We proved mirror theorems for schobers, and applied them to give new proofs of mirror symmetry for certain associated singularities. The mirror theorems were obtained using previous work of Kuwagaki on the coherent-constructible correspondence, and of Ganatra-Pardon-Shende relating constructible sheaf categories to Fukaya categories with stops.
In particular, in the previous article (a) I had used wall crossing of GIT stability to construct perverse sheaves of categories for standard flops, supported on a (partial compactification) of a certain stringy Kaehler moduli space. The starting point for our work on preprint (b) was the observation that, in the case of the resolved conifold, this construction had a natural counterpart under the coherent-constructible correspondence. We verified this for the conifold, and a further surface example, giving the claimed mirror theorems for schobers. Bondal, Kapranov, and Schechtman had previously explained how to take cohomology of certain schobers: we showed that in our cases this yielded new proofs of mirror symmetry for associated conifold and surface singularities.
(a) Perverse schobers on Riemann surfaces: constructions and examples (published in Eur. J. Math.)
(b) Mirror symmetry for perverse schobers from birational geometry, with Tatsuki Kuwagaki (FY2018, submitted)
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