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Oberseminar SoSe 2010 Zusammenfassung des Vortrags von N. Broomhead

Autoequivalences of toric surfaces

I will discuss some joint work with David Ploog in which we study autoequivalences of the derived categories of smooth, projective toric surfaces. Drawing on work of Ishii and Uehara, we show that the group of autoequivalences is generated by the standard equivalences together with spherical twists obtained from -2-curves.
I will give an outline of the proof and explain how this result is used to show that every spherical object is the cone of a morphism between exceptional objects.