An explicit construction of the McKay correspondence for \(A\)-Hilb \(\mathbb C^3\)

DOI10.1016/j.jalgebra.2004.10.001zbMath1073.14008arXivmath/0010053OpenAlexW2167197544MaRDI QIDQ1772441

Alastair Craw

Publication date: 18 April 2005

Published in: Journal of Algebra (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/math/0010053

zbMATH Keywords

toric geometryHilbert scheme of orbits

Mathematics Subject Classification ID

Toric varieties, Newton polyhedra, Okounkov bodies (14M25) Ordinary representations and characters (20C15) Global theory and resolution of singularities (algebro-geometric aspects) (14E15) Parametrization (Chow and Hilbert schemes) (14C05) (3)-folds (14J30) Classical real and complex (co)homology in algebraic geometry (14F25)

Related Items (15)

Flops of \(G\)-Hilb and equivalences of derived categories by variation of GIT quotient ⋮ Multigraded linear series and recollement ⋮ Derived Reid's recipe for abelian subgroups of \(\mathrm{SL}_3(\mathbb{C})\) ⋮ Reid's recipe and derived categories ⋮ Wall-crossing for iterated Hilbert schemes (or `Hilb of Hilb') ⋮ On Reid's recipe for non-abelian groups ⋮ On \(G/N\)-Hilb of \(N\)-Hilb ⋮ The Kähler quotient resolution of \({{\mathbb{C}}^3/ \Gamma}\) singularities, the mckay correspondence and \(D = 3\) \(\mathcal{N} = 2\) Chern-Simons gauge theories ⋮ Walls for \(G\)-Hilb via Reid's recipe ⋮ Instantons, quivers and noncommutative Donaldson-Thomas theory ⋮ The physical mirror equivalence for the local \(\mathbb P^2\) ⋮ A derived approach to geometric McKay correspondence in dimension three ⋮ Crepant resolutions of \(\mathbb{C}^3 \slash \mathbb{Z}_4\) and the generalized Kronheimer construction (in view of the gauge/gravity correspondence) ⋮ D-branes on noncompact Calabi-Yau manifolds: \(K\)-theory and monodromy ⋮ Geometric Reid's recipe for dimer models

Cites Work

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• McKay correspondence and Hilbert schemes in dimension three
• Flops of \(G\)-Hilb and equivalences of derived categories by variation of GIT quotient
• The McKay correspondence as an equivalence of derived categories
• Construction géométrique de la correspondance de McKay
• Varieties Defined by Quadratic Equations

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