Window shifts, flop equivalences and Grassmannian twists (Q2877509)

In this article, the authors study the flop of the total space of a certain kind of vector bundle on a Grassmannian to the total space of a bundle on the dual Grassmannian. They show these spaces have many derived equivalences. From these, they show that the derived category on each space has many non-trivial auto-equivalences. These auto-equivalences are algebraically constructed as window-shifts. In this case, the authors give a geometric interpretation of one of the window-shifts as a spherical twist.NEWLINENEWLINEIn order to achieve all these results, the authors first demonstrate the principles of their arguments using the example of the standard Atiyah flop in 3 dimensions. Following this, they give a clear exposition of the general heuristic argument. Finally, the authors conclude with the necessary detailed arguments.