(HoRSe seminar) Spherical objects on K3 surfaces I
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Tue, 12/10/2010 14:00 |
Daniel Huybrechts (Bonn) |
Algebraic and Symplectic Geometry Seminar  |
SR1 |
| Both parts will deal with spherical objects in the bounded derived category of coherent sheaves on K3 surfaces. In the first talk I will focus on cycle theoretic aspects. For this we think of the Grothendieck group of the derived category as the Chow group of the K3 surface (which over the complex numbers is infinite-dimensional due to a result of Mumford). The Bloch-Beilinson conjecture predicts that over number fields the Chow group is small and I will show that this is equivalent to the derived category being generated by spherical objects (which I do not know how to prove). In the second talk I will turn to stability conditions and show that a stability condition is determined by its behavior with respect to the discrete collections of spherical objects. | |||