# Fortnightly links (91)

Ciaran Meachan, Theo Raedschelders: Hochschild cohomology and deformations of $\mathbb{P}$-functors is a very interesting preprint by two authors with unprononouncable names, generalising the Huybrechts–Thomas adagium that $\mathbb{P}^n$-objects are hyperplane sections of spherical objects to the relative setting of functors. By doing so, one gets a really interesting contribution from the

*noncommutative*deformation theory of the domain category, even if one only works with geometric deformations of the codomain category. A highly recommended read if you have somewhat similar interests as me, and care about the role of Hochschild cohomology in algebraic geometry as much as I do.Genki Ouchi: Automorphism groups of cubic fourfolds and K3 categories (and in particular theorem 1.2) answers a question I asked some people 2 weeks ago at the The geometry of derived categories workshop, and it's nice to see such a concise answer. In particular, the

*automorphism group*of a cubic fourfold is isomorphic to the*subgroup*of the autoequivalence group of its K3 category*preserving a stability condition*. I'm a big fan of this slogan, and I would be very interested in seeing more instances of this phenomenon.Benjamin Antieau, Bhargav Bhatt, Akhil Mathew: Counterexamples to Hochschild–Kostant–Rosenberg in characteristic $p$ shows that one of my favourite results (namely the Hochschild–Kostant–Rosenberg decomposition)

*fails*in some examples for sufficiently small positive characteristic. This is one of the coolest results of the year for me. I might want to revisit this paper in an expository blogpost, once I've read it carefully.Laurent Manivel: Topics on the geometry of homogeneous spaces are lecture notes on recent developments, and the selection is described by the author as

largely arbitrary and mainly reflects the interests of the author

. Luckily these choices are closely aligned with what I (and hopefully you) find interesting, so they make for a very interesting read.