Full Exceptional Collections on Isotropic Grassmannians

par Lyalya Guseva

jeudi 12 juin 2025, 14:00 → 16:00 Europe/Paris

M7-411

The bounded derived category of coherent sheaves, D(X), is an important invariant of an algebraic variety X. While the structure of derived categories is generally quite intricate, in certain cases, when D(X) admits a so-called full exceptional collection, it can be described explicitly. Some of the earliest examples of full exceptional collections were constructed by Kapranov in 1983 for classical Grassmannians. Since then, a well-known conjecture has suggested that full exceptional collections consisting of vector bundles exist in the derived categories of all rational homogeneous varieties. In my talk, I will outline the proof of this conjecture for all rational homogeneous varieties associated with symplectic groups. This is joint work with Sasha Novikov.