Representing the big tilting sheaves as holomorphic Morse branes

DOI10.1016/J.AIM.2019.01.035arXiv1602.07382WikidataQ128509356 ScholiaQ128509356MaRDI QIDQ6270776

Publication date: 23 February 2016

Abstract: We introduce Morse branes in the Fukaya category of a holomorphic symplectic manifold, with the goal of constructing tilting objects in the category. We give a construction of a class of Morse branes in the cotangent bundles, and apply it to give the holomorphic branes that represent the big tilting sheaves on flag varieties.

Mathematics Subject Classification ID

Grassmannians, Schubert varieties, flag manifolds (14M15) Complex manifolds (32Q99) Presheaves and sheaves, stacks, descent conditions (category-theoretic aspects) (18F20) Symplectic aspects of mirror symmetry, homological mirror symmetry, and Fukaya category (53D37) Derived categories of sheaves, dg categories, and related constructions in algebraic geometry (14F08)

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