Matrix factorisations: Knörrer’s periodicity and beyond.

Martin Kalck (University of Edinburgh)

Wednesday 18th November, 2015 16:00-17:00 Maths 522


We give an (elementary) introduction to matrix factorisations focusing on motivations and examples.

Knörrer’s periodicity relates matrix factorisations of a polynomial f with matrix factorisations of a polynomial g = f + y^2 + z^2. Using work of Buchweitz & Eisenbud this can also be viewed as an equivalence of singularity categories of the corresponding hypersurface singularities defined by f and g respectively. In joint work with Joe Karmazyn we obtain a similar equivalence for all cyclic quotient singularities in Krull dimension 2, which also gives a new proof of Knörrer’s periodicity in the well studied case of Kleinian singularities in type A  (ie the case of a cyclic subgroup of SL_2).

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