# Fortnightly links (99)

Alexander Kuznetsov, Maxim Smirnov: Residual categories for (co)adjoint Grassmannians in classical types is a cool paper, explaining how the structure of minimal Lefschetz exceptional collections for generalised Grassmannians is reflected by the finer structure in the quantum cohomology of these variaties, and constructs the first (proven to be full) exceptional collection for $\mathrm{OGr}(2,2n)$. Cool stuff!

Andreas Hochenegger, Ciaran Meachan: Frobenius and spherical codomains and neighbourhoods constructs interesting subcategories of the derived category of a smooth projective variety, associated to natural functors of geometric origin,

*which are usually not admissible*. In my usual setting, all subcategories are automatically admissible (because everything I consider has a Serre functor, usually), but this fails in these examples. This is intriguing me, and I'd love to understand these categories better.Max Lieblich, Martin Olsson: Derived categories and birationality studies when a derived equivalence means that varieties are birational. In low dimensions (i.e. up to dimension 2), we know that derived equivalent means isomorphic. But already for Calabi–Yau 3-folds there exist derived equivalent examples which are not birational (which leads to many interesting constructions in the Grothendieck ring of varieties, but that is a different topic). As summarised in question 1.10, the idea is that a derived equivalence which preserves the codimension filtration on cohomological realisations is a way of recognising that the varieties are birational. Interesting stuff!