Translator Disclaimer
15 May 2001 Braid group actions on derived categories of coherent sheaves
Paul Seidel, Richard Thomas
Duke Math. J. 108(1): 37-108 (15 May 2001). DOI: 10.1215/S0012-7094-01-10812-0

Abstract

This paper gives a construction of braid group actions on the derived category of coherent sheaves on a variety $X$. The motivation for this is M. Kontsevich's homological mirror conjecture, together with the occurrence of certain braid group actions in symplectic geometry. One of the main results is that when dim $X\geq 2$, our braid group actions are always faithful.

We describe conjectural mirror symmetries between smoothings and resolutions of singularities which lead us to find examples of braid group actions arising from crepant resolutions of various singularities. Relations with the McKay correspondence and with exceptional sheaves on Fano manifolds are given. Moreover, the case of an elliptic curve is worked out in some detail.

Citation

Download Citation

Paul Seidel. Richard Thomas. "Braid group actions on derived categories of coherent sheaves." Duke Math. J. 108 (1) 37 - 108, 15 May 2001. https://doi.org/10.1215/S0012-7094-01-10812-0

Information

Published: 15 May 2001
First available in Project Euclid: 5 August 2004

zbMATH: 1092.14025
MathSciNet: MR1831820
Digital Object Identifier: 10.1215/S0012-7094-01-10812-0

Subjects:
Primary: 14F05
Secondary: 14J32 , 18E30 , 20F36 , 53D40

Rights: Copyright © 2001 Duke University Press

JOURNAL ARTICLE
72 PAGES

This article is only available to subscribers.
It is not available for individual sale.
+ SAVE TO MY LIBRARY

SHARE
Vol.108 • No. 1 • 15 May 2001
Back to Top