# Fortnightly links (142)

Alexander Kuznetsov: Semiorthogonal decompositions in families is a writeup for next year's ICM, on the recent breakthroughs on semiorthogonal decompositions in algebraic geometry obtained by Sasha Kuznetsov and collaborators. It is an absolutely splendid read, and I strongly recommend it to any reader of this blog interested in semiorthogonal decompositions.

This also means that more ICM articles are going to appear. Here's an incomplete list of submissions which are possibly of interest to what I think is my audience:

- Aravind Asok, Jean Fasel: Vector bundles on algebraic varieties
- Yiannis Sakellaridis: Spherical varieties, functoriality, and quantization
- Olivier Wittenberg: Some aspects of rational points and rational curves
- Yuri Prokhorov: Effective results in the three-dimensional minimal model program

I will try to update this list as I see more contributions appear. Highlights will be featured in future fortnightly links.

Gavin Brown, Michael Wemyss: Local normal forms of noncommutative functions is a cool paper classifying noncommutative singularities, up to isomorphism of their Jacobi algebras. Aside from the coolness of the results, there is an inspiring Twitter thread by one of the authors.

Mitchell Faulk, Chiu-Chu Melissa Liu: Embedding Deligne-Mumford stacks into GIT quotient stacks of linear representations gives a really nice answer to the question "what is a polarisation of a proper Deligne-Mumford stack?" They show how the answer is a closed embedding into some $[\mathbb{A}^{\mathrm{ss}}/\mathrm{GL}_r]$ for a vector bundle of rank $r$, provided by a relatively ample vector bundle for the map to the coarse moduli space. This nicely subsumes the usual embedding by an ample line bundle into projective space, or by an ample vector bundle into a Grassmannian. Fun!