Pieter Belmans
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Fortnightly links (36)

May 14, 2017 • Pieter Belmans

posted in:
  • mathematics
tags:
  • fortnightly links
  • 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.

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