Geometric Reid's recipe for dimer models - Alastair Craw
- 11 years ago
Date: Tuesday 4th June 2013
Speaker: Alastair Craw (Bath)
Title: Geometric Reid's recipe for dimer models
Abstract: A consistent dimer model on a real 2-torus determines a CY3 algebra A whose centre defines a Gorenstein toric threefold X. Results of Ishii-Ueda show that every projective crepant resolution of X can be constructed as a fine moduli space of A-modules such that the tautological bundle T on the moduli space is a tilting bundle. I'll explain what is known about the image of the vertex simple A-modules under a derived equivalence induced by T for the moduli space defined by a special stability parameter. When A is the skew group algebra of a finite abelian subgroup G in SL(3,C), this moduli space is the G-Hilbert scheme, and our results extend work of Cautis-Logvinenko and Logvinenko on 'Geometric Reid's recipe'. Our proof uses variation of GIT quotient and is rather different from the original work of Cautis and Logvinenko. This is joint work with Raf Bocklandt and Alex Quintero Velez.
http://www.maths.ed.ac.uk/cheltsov/seminar/
Speaker: Alastair Craw (Bath)
Title: Geometric Reid's recipe for dimer models
Abstract: A consistent dimer model on a real 2-torus determines a CY3 algebra A whose centre defines a Gorenstein toric threefold X. Results of Ishii-Ueda show that every projective crepant resolution of X can be constructed as a fine moduli space of A-modules such that the tautological bundle T on the moduli space is a tilting bundle. I'll explain what is known about the image of the vertex simple A-modules under a derived equivalence induced by T for the moduli space defined by a special stability parameter. When A is the skew group algebra of a finite abelian subgroup G in SL(3,C), this moduli space is the G-Hilbert scheme, and our results extend work of Cautis-Logvinenko and Logvinenko on 'Geometric Reid's recipe'. Our proof uses variation of GIT quotient and is rather different from the original work of Cautis and Logvinenko. This is joint work with Raf Bocklandt and Alex Quintero Velez.
http://www.maths.ed.ac.uk/cheltsov/seminar/