Fortnightly links (120)

Yujiro Kawamata: On the derived category of a weighted projective threefold is a short note, constructing a semiorthogonal decomposition for $\mathbb{D}^{\mathrm{b}}(\mathbb{P}(1,1,1,3))$. This singular threefold could be seen as the first (formerly) open case, whose singularities were outside the scope of earlier results.

Olivier Debarre, Giovanni Mongardi: Gushel-Mukai varieties with many symmetries and an explicit irrational Gushel-Mukai threefold constructs an explicit irrational Gushel–Mukai threefold (it was only known that a generic one is not rational, but not a single non-rational example was constructed), by showing that the automorphism group of a certain Gushel–Mukai threefold and its induced intermediate Jacobian is too big to ever be the Jacobian of a curve of genus 10 (which it would have to be if it were rational, by the Clemens–Griffiths criterion). Great!

Some news from the Lean front: Schemes in Lean discusses the various approaches that have been taken to define schemes in Lean, and why some are better than others. And The end of the summer discusses the progress Buzzard's students have made in 2020. It is amazing to see this!