Moduli of McKay quiver representations. II: Gröbner basis techniques

DOI10.1016/j.jalgebra.2007.02.014zbMath1161.14038arXivmath/0611840OpenAlexW2050663957MaRDI QIDQ2464488

Diane MacLagan, Alastair Craw, Rekha R. Thomas

Publication date: 21 December 2007

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

Full work available at URL: https://arxiv.org/abs/math/0611840

zbMATH Keywords

Gröbner bases\(G\)-Hilbert schemeMcKay quiver

Mathematics Subject Classification ID

Toric varieties, Newton polyhedra, Okounkov bodies (14M25) Gröbner bases; other bases for ideals and modules (e.g., Janet and border bases) (13P10) Representations of quivers and partially ordered sets (16G20)

Related Items

Terminal quotient singularities in dimension three via variation of GIT, Homological dimensions for co-rank one idempotent subalgebras, Hilbert basis resolutions for three-dimensional canonical cyclic quotient singularities, The power of pyramid decomposition in Normaliz, On the Craw-Ishii conjecture, McKay quivers and Lusztig algebras of some finite groups, Instantons, quivers and noncommutative Donaldson-Thomas theory, Cellular resolutions of noncommutative toric algebras from superpotentials., Construction of G-Hilbert schemes, Derived McKay correspondence via pure-sheaf transforms, Superpotentials and higher order derivations., On monotonicity of F-blowup sequences, THE G-HILBERT SCHEME FOR, Mastering the master space, Lecture notes on quivers with superpotential and their representations, Preprojective algebra structure on skew-group algebras, Morita theorem for hereditary Calabi-Yau categories

Uses Software

• Macaulay2
• Normaliz
• Gfan
• GRIN

Cites Work

• The construction of ALE spaces as hyper-Kähler quotients
• McKay correspondence and Hilbert schemes in dimension three
• Combinatorics of the toric Hilbert scheme
• Toric Hilbert schemes.
• Flops of \(G\)-Hilb and equivalences of derived categories by variation of GIT quotient
• Non-connected toric Hilbert schemes
• The McKay correspondence as an equivalence of derived categories
• On the McKay correspondence for a finite small subgroup of GL(2,ℂ)
• Multigraded Hilbert schemes
• GRIN: An implementation of Gröbner bases for integer programming
• Moduli of McKay quiver representations I: the coherent component
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