Abstract des Vortrages von Arend Bayer
The space of stability conditions on abelian threefolds (and on some Calabi-Yau threefolds)
The problem of constructing Bridgeland stability conditions on smooth projective threefolds is on the one hand perhaps the biggest open problem in the theory; on the other hand, it is related to deep questions about their geometry (Fujita's conjecture and Reider-type theorems). In this talk, I will explain recent joint work with Emanuele Macri and Paolo Stellari on this topic.
We strengthen and clarify a conjectural approach towards their construction for arbitrary threefolds. Then, generalizing a result by Maciocia and Piyaratne, we prove this conjecture for arbitrary abelian threefolds, and for Calabi-Yau threefolds obtained as (resolutions) of finite quotients of abelian threefolds. This also leads to a description of a complete connected component of the space of stabiliy conditions in these cases.