Calabi-Yau structures, spherical functors, and shifted symplectic structures

DOI10.1016/j.aim.2021.108037zbMath1490.14061arXiv1701.07789OpenAlexW3202648275MaRDI QIDQ2237411

Theodore Spaide, Pranav Pandit, Ludmil Katzarkov

Publication date: 27 October 2021

Published in: Advances in Mathematics (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1701.07789

zbMATH Keywords

Fukaya-Seidel categoriesPicard-Lefschetz theoryCalabi-Yau structuresderived geometryperverse schobersspherical functors

Mathematics Subject Classification ID

Calabi-Yau manifolds (algebro-geometric aspects) (14J32) Symplectic aspects of mirror symmetry, homological mirror symmetry, and Fukaya category (53D37) Fundamental constructions in algebraic geometry involving higher and derived categories (homotopical algebraic geometry, derived algebraic geometry, etc.) (14A30) Derived categories of sheaves, dg categories, and related constructions in algebraic geometry (14F08)

Related Items (3)

Some new categorical invariants ⋮ Perverse sheaves of categories and some applications ⋮ Perverse schobers on Riemann surfaces: constructions and examples

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Shifted symplectic structures
• Mapping class group and a global Torelli theorem for hyperkähler manifolds
• Derived algebraic geometry
• Topological conformal field theories and Calabi-Yau categories
• Quasi-Hamiltonian reduction via classical Chern-Simons theory
• Fukaya categories and Picard-Lefschetz theory
• \({\mathcal D}\)-modules et faisceaux pervers dont le support singulier est un croisement normal
• Hyperkähler metrics and supersymmetry
• Lefschetz fibrations in symplectic geometry
• Logarithmic deformations of normal crossing varieties and smoothing of degenerate Calabi-Yau varieties
• Calabi-Yau and fractional Calabi-Yau categories
• Enriched \(\infty\)-categories via non-symmetric \(\infty\)-operads
• Spherical DG-functors
• Perverse schobers and birational geometry
• Families of Lagrangian fibrations on hyperkähler manifolds
• Algebraic string operations
• The Geometry of the Master Equation and Topological Quantum Field Theory
• Lagrangian structures on mapping stacks and semi-classical TFTs
• REPRESENTABLE FUNCTORS, SERRE FUNCTORS, AND MUTATIONS
• Hodge theoretic aspects of mirror symmetry
• Notes on A∞-Algebras, A∞-Categories and Non-Commutative Geometry
• On the Classification of Topological Field Theories
• The Self-Duality Equations on a Riemann Surface
• Métriques kählériennes et fibrés holomorphes
• Fukaya A ∞-structures Associated to Lefschetz Fibrations. II
• Mirror symmetry, Tyurin degenerations and fibrations on Calabi-Yau manifolds
• Homological Algebra of Mirror Symmetry
• Relative Calabi–Yau structures
• Moduli of objects in dg-categories
• Higher Topos Theory (AM-170)

This page was built for publication: Calabi-Yau structures, spherical functors, and shifted symplectic structures