A periodic table of (generalised) Grassmannians.
$\OGr_+(7,14)\hookrightarrow\mathbb{P}^{ 63 }$
No full exceptional collection is known for $\mathbf{D}^{\mathrm{b}}(\OGr_+(7,14))$. Will you be the first to construct one? Let us know if you do!
Kuznetsov–Polishchuk have constructed an exceptional collection of maximal length in MR3463417. Can you prove it's full?
The small quantum cohomology is generically semisimple.
The big quantum cohomology is generically semisimple.
The eigenvalues of quantum multiplication by $\mathrm{c}_1(\OGr_+(7,14))$ are given by: