A belated fortnightly links, to be blamed on SPONGE (Stacks Project ONline Geometry workshop), which was a great experience!

  • Ugo Bruzzo, Daniel Hernandez Ruiperez, Alexander Polishchuk: Notes on fundamental algebraic supergeometry. Hilbert and Picard superschemes discusses many aspects of supergeometry, in a language that I as an ordinary algebraic geometer can read fluently. This is great! This makes learning something about supergeometry much easier, because in my (very) limited experience most references usually do things quite ad-hoc for the purposes of said reference, without a global picture.

    Time for someone to start a Superstacks project...

  • Osamu Iyama, Michael Wemyss: Tits cone intersections and applications seems to be a preprint of a book. A book containing some of the most beautiful mathematical pictures I have ever seen. Aside from the pretty pictures, it also has beautiful mathematics, elaborating on the recent work of the authors on relating tilting theory to birational geometry.

    This looks like excellent material for a reading seminar.

  • Kenta Ueyama: Derived categories of skew quadric hypersurfaces proves the at first surprising result that $\mathbf{D}^{\mathrm{b}}(\operatorname{qgr}A)$ where $A$ is the quotient of a specific skew polynomial algebra by a central quadratic equation can have more exceptional objects than the derived category of a commutative quadric. In particular, these skew quadric hypersurfaces are not supposed to be deformations of ordinary quadrics! This is a very intriguing picture that I'd love to understand more.

This is a frustrating fortnightly links, because I would like to get to the bottom of all three references, but there is only so much time in a day...