Shinnosuke Okawa, Semiorthogonal Decompositions and Relative Canonical Base Locus

Motivated by the DK hypothesis, some years ago I proved that SODs of the derived category of a smooth projective variety are strongly constrained by the base locus of the canonical linear system. In particular, this leads to the indecomposability of the derived category of varieties whose canonical bundles are globally generated (hence minimal). In this talk I will briefly recall this work and discuss its generalization to the relative settings. The latter implies new indecomposability results, including the case of minimal surfaces of positive irregularity. This talk is based on arXiv:2304.14048.