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Seminar of the Department of Algebra and of the Department of Algebraic Geometry (Shafarevich Seminar)
May 15, 2012 15:00, Moscow, Steklov Mathematical Institute, room 540 (Gubkina 8)
 


Derived categories and symmetry: Grassmannians

Will Donovan

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Abstract: We describe a straightforward algebraic procedure for constructing interesting symmetries of a particular derived category, specifically the derived category of coherent sheaves on the total space of a certain vector bundle over a Grassmannian. This can be thought of as a natural alabi–Yau category associated to the Grassmannian. We refer to our procedure as “window shifting”.
To explicitly describe the effect of a window shift we use some interesting complexes of locally free sheaves on the Grassmannian, variously known as staircase or Lascoux complexes. If there is time, we will also give a geometric description of the window shifts in terms of spherical twists, and explain how we hope to generalize our methods to a much wider class of examples. This is joint work with Ed Segal.

Language: English

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