Pieter Belmans—Fortnightly links (42)

Max Lieblich, Moduli of sheaves: a modern primer is Max's contribution to the proceedings of the AMS summer institute in Salt Lake City. Whenever he gets the chance, he likes to introduce funny terminology for things, and this preprint contributes the term merbe to the algebraic geometry vocabulary (which is either a $\mathbf{G}_{\mathrm{m}}$- or $\mu_n$-gerbe). He also has an important piece of advice for students of algebraic stacks in §1.2.
Alexander Kuznetsov, Derived categories of families of sextic del Pezzo surfaces is a generalisation of the description of a (smooth) sextic del Pezzo surface over a non-algebraically closed field (due to Blunk–Sierra–Smith and Auel–Bernardara) to arbitrary flat families with mild singularities. Awesome!
The past week we had the Stacks project workshop, I'll discuss more about it next week, but one of the goals was to get people working in groups on a topic related to algebraic stacks and potentially turn this into a section or chapter of the Stacks project. The public repositories that I am aware of are
- Johan de Jong's group, Examples of complete moduli stacks
- Davesh Maulik's group, Projectivity of $\overline{\mathcal{M}}_g$
The progress they made is truly impressive.