Non-commutative desingularization of determinantal varieties. I

DOI10.1007/s00222-010-0258-7zbMath1204.14003arXiv0911.2659OpenAlexW1975068388MaRDI QIDQ993385

Michel Van den Bergh, Graham J. Leuschke, Ragnar-Olaf Buchweitz

Publication date: 10 September 2010

Published in: Inventiones Mathematicae (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/0911.2659

zbMATH Keywords

quiversClifford algebrasimple representationsmaximal Cohen-Macaulaynon-commutative desingularizationsparse spectral sequencetautological Koszul complex

Mathematics Subject Classification ID

Noncommutative algebraic geometry (14A22) Rings arising from noncommutative algebraic geometry (16S38) Global theory and resolution of singularities (algebro-geometric aspects) (14E15) Riemann-Roch theorems (14C40) Representations of quivers and partially ordered sets (16G20) Syzygies, resolutions, complexes and commutative rings (13D02) Cohen-Macaulay modules (13C14)

Related Items

Homological projective duality for determinantal varieties, Computing global dimension of endomorphism rings via ladders, Noncommutative resolutions and rational singularities, Non-commutative crepant resolution of minimal nilpotent orbit closures of type A and Mukai flops, Non-commutative resolutions of quotient singularities for reductive groups, Predictions for Gromov-Witten invariants of noncommutative resolutions, Categorical and K-theoretic Donaldson–Thomas theory of (part II), Noncommutative crepant resolutions, an overview, Categorical resolutions of a class of derived categories, Noncommutative enhancements of contractions, Semi-steady non-commutative crepant resolutions via regular dimer models, Partial local resolution by characteristic zero methods, Local Euler obstructions and Chern–Mather classes of determinantal varieties, Gorenstein and totally reflexive orders, On the Abuaf-Ueda flop via non-commutative crepant resolutions, Noncommutative resolutions of discriminants, Algebras and varieties, Derived categories of projectivizations and flops, The cohomology annihilator of a curve singularity, Noncommutative (crepant) desingularizations and the global spectrum of commutative rings

Uses Software

• PieriMaps

Cites Work

• Three-dimensional flops and noncommutative rings
• Non-commutative Donaldson-Thomas invariants and the conifold
• Derived equivalences by quantization
• Ideals defined by matrices and a certain complex associated with them
• Fomin-Zelevinsky mutation and tilting modules over Calabi-Yau algebras
• Generic maps revised
• HOMOLOGICAL PROPERTIES OF ASSOCIATIVE ALGEBRAS: THE METHOD OF HELICES
• Resultants and Chow forms via exterior syzygies
• Endomorphism Rings of Finite Global Dimension
• A Generalized Koszul Complex. II. Depth and Multiplicity
• Factoring the adjoint and maximal Cohen-Macaulay modules over the generic determinant
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