Fortnightly links (36)

Jørgen Vold Rennemo, Ed Segal, Michel Van den Bergh: A non-commutative Bertini theorem is a nice little preprint which shows that there is a Bertini-type result for noncommutative (crepant) resolutions, i.e. they show that if you have a normal variety $X$ with a coherent sheaf of algebras $\mathcal{A}$ which is a noncommutative (crepant) resolution, and a map $X\to {\mathbb{P}}^n$, then for a generic hyperplane $H\subseteq {\mathbb{P}}^n$ the fibre product $X{\times }_{{\mathbb{P}}^n}H$ together with the sheaf of algebras obtained by pullback is again a noncommutative (crepant) resolution. Cool!

Anthony Blanc, Ludmil Katzarkov, Pranav Pandit: Generators in formal deformations of categories concerns compact generators in triangulated ategories, one of my favourite subjects. In this paper they show that if you take a formal deformation over $k[[t]]$, then if you have a sufficiently nice compact generator downstairs, you obtain one for the deformation. It is closely related to the notion of curvature, as addressed in Wendy Lowen, Michel Van den Bergh: The curvature problem for formal and infinitesimal deformations, and I'd like to really grok what is going in both papers.

In case you missed it (which is unlikely, given the media attention), here are Grothendieck's notes as collected by the University of Montpellier.