Emanuele Macri : Stability conditions on abelian threefolds

Posted by Izzet Coskun , part of the Algebraic Geometry Seminar.

At

Dec. 3, 2014, 4 p.m.

In

SEO 427

Abstract

I will present a new proof and a generalization a result by Maciocia and Piyaratne on the existence of Bridgeland stability conditions on any abelian threefold. As an application, we deduce the existence of Bridgeland stability conditions on a number of Calabi-Yau threefolds, namely Calabi-Yau threefolds of abelian type and Kummer threefolds. As in the work of Maciocia and Piyaratne, the idea is to show a Bogomolov-Gieseker type inequality involving Chern classes of certain stable objects in the derived category; this was conjectured by Bayer, Toda, and myself. Our approach uses the multiplication maps on abelian threefolds instead of Fourier-Mukai transforms. This is joint work with Arend Bayer and Paolo Stellari.