3 problems

Let $Q\to S$ be a quadric surface bundle over an integral Noetherian scheme. Assume that the bundle has simple degeneration generically and that each fibre has corank at most $2$.…

Let $p\colon \mathcal{Q}\to S$ be a quadric surface bundle. Write $S_2$ and $S_3$ for the loci where the fibers have corank at least $2$ and $3$, respectively, and let…

Quadric-bundle phantom-category conjecture. The semiorthogonal decomposition of the derived category of such a degeneration contains a phantom category.