Mirror symmetry for perverse schobers from birational geometry

Abstract

Perverse schobers are categorical analogs of perverse sheaves. Examples arise from varieties admitting flops, determined by diagrams of derived categories of coherent sheaves associated to the flop: in this paper we construct mirror partners to such schobers, determined by diagrams of Fukaya categories with stops, for examples in dimensions 2 and 3. Interpreting these schobers as supported on loci in mirror moduli spaces, we prove homological mirror symmetry equivalences between them. Our construction uses the coherent-constructible correspondence and a recent result of Ganatra-Pardon-Shende to relate the schobers to certain categories of constructible sheaves. As an application, we obtain new mirror symmetry proofs for singular varieties associated to our examples, by evaluating the categorified cohomology operators of Bondal-Kapranov-Schechtman on our mirror schobers.

arXiv comment38 pages, 6 figures

References in corpus (16)

• Semiorthogonal decomposition for algebraic varieties
• Semiorthogonal decompositions in algebraic geometry
• Mukai implies McKay: the McKay correspondence as an equivalence of derived categories
• Wrapped microlocal sheaves on pairs of pants
• Smooth toric DM stacks
• Microlocal Morse theory of wrapped Fukaya categories
• A Point's Point of View of Stringy Geometry
• The nonequivariant coherent-constructible correspondence for toric stacks
• Mirror symmetry for very affine hypersurfaces
• K-Theoretic and Categorical Properties of Toric Deligne--Mumford Stacks
• The special McKay correspondence and exceptional collection
• Perverse sheaves of categories and some applications
• Lagrangian Skeleta of Hypersurfaces in $({\mathbb{C}}^{\ast }{)}^n$
• Derived categories of toric varieties III
• Perverse schobers on Riemann surfaces: constructions and examples
• Gluing semi-orthogonal decompositions

Cited by in corpus (1)

• A class of perverse schobers in Geometric Invariant Theory