Derived categories of threefolds near the Noether line

Abstract

We show that derived categories of canonical stacks associated to general threefolds in the principal component of the moduli space of canonical threefolds on the refined Noether line are semiorthogonally indecomposable. First we generalize a criterion of Kawatani-Okawa for the indecomposability of derived categories of surfaces of general type to higher-dimensional varieties and stacks. And then we generalize a construction of Kobayashi and Hu-Zhang and a classification result of Coughlan-Pignatelli to the second and third Noether lines to show that our criterion applies to these canonical stacks.