Algebraic Geometry Seminar

Graham LeuschkeSyracuse University
Extensions of theorems of Knörrer and Herzog-Popescu, with an application to noncommutative hypersurfaces

Wednesday, October 4, 2017 - 1:20pm
Malott 205

Knörrer periodicity asserts a tight relationship between matrix factorizations of $f$ and the double branched cover $f+z^2$. I will describe a generalization, relating matrix factorizations of $f$ and matrix factorizations of $f+z^n$. For each $k =1, \dots, n$ we obtain a functorially finite (“approximating”) subcategory of matrix factorizations of $f+z^n$. The case of $k=1$ and an ADE singularity $f$ leads to a class of noncommutative rings over which every minimal projective resolution is eventually periodic of period 2, suggesting that they might be called noncommutative hypersurfaces. This is joint work with Alex Dugas (U. Pacific).