Algebraic Geometry Seminar
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).