The odd biisotropic symplectic Grassmannian $\operatorname{S_2Gr}(3,7)$

Abstract

We introduce a class of interesting algebraic varieties --- odd biisotropic symplectic Grassmannians $\operatorname{S_2Gr}(k,2n+1)$ and study them with an emphasis on the case of the submaximal odd biisotropic symplectic Grassmannians $\operatorname{S_2Gr}(n,2n+1)$, which we call catalecticant varieties. The main result of the paper is a construction of a full exceptional collection in the derived category of the catalecticant sixfold $\operatorname{S_2Gr}(3,7)$.