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Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)

 

Autoequivalences of toric surfaces


Authors: Nathan Broomhead and David Ploog
Journal: Proc. Amer. Math. Soc. 142 (2014), 1133-1146
MSC (2010): Primary 14J26, 14M25, 18E30
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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Additional Information

Nathan Broomhead
Affiliation: Institut für Algebraische Geometrie, Leibniz Universität Hannover, Welfengarten 1, 30167 Hannover, Germany
Email: broomhead@math.uni-hannover.de

David Ploog
Affiliation: Institut für Algebraische Geometrie, Leibniz Universität Hannover, Welfengarten 1, 30167 Hannover, Germany
Address at time of publication: Fakultät für Mathematik, Algebraische Geometrie, Universität Duisburg-Essen, 45177 Essen, Germany
Email: david.ploog@uni-due.de

DOI: http://dx.doi.org/10.1090/S0002-9939-2014-11530-9
PII: S 0002-9939(2014)11530-9
Keywords: Toric surface, derived category, group of autoequivalences, exceptional object
Received by editor(s): June 8, 2011
Received by editor(s) in revised form: September 22, 2011, October 25, 2011, February 14, 2012, and May 11, 2012
Published electronically: January 30, 2014
Additional Notes: The second author was supported by DFG priority program 1388 “Darstellungstheorie”
Communicated by: Lev Borisov
Article copyright: © Copyright 2014 American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication.