ncts

The MMP aims at classifying algebraic varieties up to birational equivalence, and derived categories are rich homological invariants of algebraic varieties that see a lot of their birational geometry. The basic operations of the MMP are reflected as semiorthogonal decompositions in the derived category, and minimal varieties of non-zero geometric genus are conjectured to have indecomposable derived categories. Hyperelliptic surfaces are an interesting example, because they show that the converse of the conjecture does not hold. In this talk, we discuss a generalization of the indecomposability of hyperelliptic surfaces to higher dimensional hyperelliptic manifolds, which is current joint work in progress with Pieter Belmans and Andreas Demleitner.The talk will be roughly divided into three parts. First, an introductory part in which derived categories are briefly introduced, focusing on their relation to birational geometry. Then, an overview of semiorthogonal decompositions and their relation to the MMP. And lastly, a more detailed discussion of the semiorthogonal indecomposability question.