Autoequivalences of toric surfaces

Broomhead, Nathan; Ploog, David

doi:10.1090/S0002-9939-2014-11530-9

Autoequivalences of toric surfaces
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by Nathan Broomhead and David Ploog

Proc. Amer. Math. Soc. 142 (2014), 1133-1146

DOI: https://doi.org/10.1090/S0002-9939-2014-11530-9

Published electronically: January 30, 2014

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Abstract:

We show that the autoequivalence group of the derived category of any smooth projective toric surface is generated by the standard equivalences and spherical twists obtained from $-2$-curves. In many cases we give all relations between these generators. We also prove a close link between spherical objects and certain pairs of exceptional objects.

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