On the derived category of the adjoint Grassmannian of type F

Abstract

We construct a full rectangular Lefschetz collection in the derived category of the adjoint Grassmannian in type ${\mathrm{F}}_4$. This gives the first example of a full exceptional collection on this variety and also completes the proof of a conjecture due to Alexander Kuznetsov and the author that relates the structure of the derived category of coherent sheaves to the small quantum cohomology in the case of adjoint varieties for non-simply laced groups.

v4: dedication added; v3: minor improvements; v2: minor improvements throughout the text, introduction made more precise, section 4 reorganised and clarified

References in corpus (2)

• Full exceptional collections on Lagrangian Grassmannians
• Derived categories of the Cayley plane and the coadjoint Grassmannian of type F