Noncommutative deformations and flops

DOI10.1215/00127094-3449887zbMath1346.14031arXiv1309.0698OpenAlexW1592798054MaRDI QIDQ726774

Michael Wemyss, Will Donovan

Publication date: 14 July 2016

Published in: Duke Mathematical Journal (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1309.0698

zbMATH Keywords

flipsflopsDynkin typeanalytic equivalence typescontraction algebraderived autoequivalencenoncommutative deformation algebranoncommutative deformation theory

Mathematics Subject Classification ID

Related Items (45)

Deformations of rational surface singularities and reflexive modules with an application to flops ⋮ Contractions of 3-folds: Deformations and invariants ⋮ Noncommutative Deformations of Thick Points ⋮ Singularity categories via the derived quotient ⋮ Gopakumar-Vafa invariants do not determine flops ⋮ Non-commutative crepant resolution of minimal nilpotent orbit closures of type A and Mukai flops ⋮ Spherical DG-functors ⋮ On multi-pointed non-commutative deformations and Calabi–Yau threefolds ⋮ Hochschild (co)homology and derived categories ⋮ Adjoints to a Fourier-Mukai functor ⋮ Perverse schobers and birational geometry ⋮ Flops and spherical functors ⋮ Non-commutative width and Gopakumar-Vafa invariants ⋮ Stability conditions for contraction algebras ⋮ Flops and the S-duality conjecture ⋮ Relating derived equivalences for simplices of higher-dimensional flops ⋮ Flops and clusters in the homological minimal model programme ⋮ A lockdown survey on cDV singularities ⋮ Stability conditions for 3-fold flops ⋮ Homotopical algebra and higher structures. Abstracts from the workshop held September 19--25, 2021 (hybrid meeting) ⋮ Unnamed Item ⋮ On the finiteness of the derived equivalence classes of some stable endomorphism rings ⋮ Noncommutative enhancements of contractions ⋮ The length classification of threefold flops via noncommutative algebras ⋮ Discreteness of silting objects and t-structures in triangulated categories ⋮ POTENTIAL ALGEBRAS WITH FEW GENERATORS ⋮ Growth, entropy and commutativity of algebras satisfying prescribed relations. ⋮ Contraction algebra and singularity of three-dimensional flopping contraction ⋮ Mukai flops and \(\mathbb{P}\)-twists ⋮ Genus zero Gopakumar-Vafa invariants from open strings ⋮ On non-commutative formal deformations of coherent sheaves on an algebraic variety ⋮ The tilting theory of contraction algebras ⋮ Faithful actions from hyperplane arrangements ⋮ Mutation of frozen Jacobian algebras ⋮ Lecture notes on quivers with superpotential and their representations ⋮ Universal functors on symmetric quotient stacks of abelian varieties ⋮ Derived categories of projectivizations and flops ⋮ Quasi-homogeneity of potentials ⋮ Perverse schobers on Riemann surfaces: constructions and examples ⋮ Non-commutative deformations of simple objects in a category of perverse coherent sheaves ⋮ Dehn twists and Lagrangian spherical manifolds ⋮ Golod–Shafarevich-Type Theorems and Potential Algebras ⋮ The derived deformation theory of a point ⋮ Non-commutative deformations of perverse coherent sheaves and rational curves ⋮ Non-commutative thickening of moduli spaces of stable sheaves

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Quivers from matrix factorizations
• Maximal modifications and Auslander-Reiten duality for non-isolated singularities
• Growth, entropy and commutativity of algebras satisfying prescribed relations.
• Deformation theory of objects in homotopy and derived categories. III: Abelian categories
• Three-dimensional flops and noncommutative rings
• Deformation theory of objects in homotopy and derived categories. I: General theory
• Fourier--Mukai transforms for Gorenstein schemes
• Non-commutative width and Gopakumar-Vafa invariants
• Orthogonally spherical objects and spherical fibrations
• The \(A_\infty\) deformation theory of a point and the derived categories of local Calabi-Yaus
• Deformation theory of objects in homotopy and derived categories. II: Pro-representability of the deformation functor
• The classification of special Cohen-Macaulay modules
• Relative integral functors for singular fibrations and singular partners
• Noncommutative deformations of modules
• Flops and derived categories.
• Flops and equivalences of derived categories for threefolds with only terminal Gorenstein singularities.
• Braid group actions on derived categories of coherent sheaves.
• General hyperplane sections of nonsingular flops in dimension 3
• Singular derived categories of \(\mathbb{Q}\)-factorial terminalizations and maximal modification algebras
• The McKay correspondence as an equivalence of derived categories
• Hochschild (co-)homology of schemes with tilting object
• Deformation theory of abelian categories
• Stability conditions and crepant small resolutions
• On a certain generalization of spherical twists
• Fomin-Zelevinsky mutation and tilting modules over Calabi-Yau algebras
• Computing Noncommutative Deformations of Presheaves and Sheaves of Modules
• Homological Algebra on a Complete Intersection, with an Application to Group Representations
• Classification of Three-Dimensional Flips

This page was built for publication: Noncommutative deformations and flops