Fortnightly links (96)
Olivier Debarre: Gushel–Mukai varieties is an overview article on Gushel–Mukai varieties, written by one of the leading figures in the study of their geometric, mdular, Hodge-theoretic and derived categorical properties. They form a very interesting class of Fano varieties, with exciting links to hyperkähler varieties. The notes summarise several (long) papers by the author, jointly with Alexander Kuznetsov, and the links to other works, and form a very nice read to get familiar with the state-of-the-art.
Špela Špenko, Michel Van den Bergh: Comparing the Kirwan and noncommutative resolutions of quotient varieties shows that the noncommutative crepant resolutions for reductive quotient singularities constructed earlier by them are minimal, in the sense that their derived categories embed fully faithfully in the derived categories of the stacky Kirwan resolutions (which are not minimal). Cool stuff!
Andrea Petracci: On deformations of toric Fano varieties is a nice overview article on deformation theory of mildly singular varieties, which then applies the machinery to study deformations of toric Fano varieties. It also determines for all 4319 reflexive Fano polytopes of dimension 3 whether they are smooth, have isolated Gorenstein singularities, ordinary double points, or are not smoothable for various reasons.