Mathematics

We show how to associate to a smooth projective morphism $X/U$ a functor on $(Sch/U)$ sending $V/U$ to the set of semiorthogonal decompositions on $Perf(X_V)$. We show this functor defines an étale algebraic space over $U$. As an application, we determine a range of integers $k$ for which the symmetric products $Sym^k(C)$ admit no semiorthogonal decompositions, for $C$ a smooth projective curve. Joint work with Pieter Belmans and Shinnosuke Okawa.