Translator Disclaimer
15 April 2004 Three-dimensional flops and noncommutative rings
Michel Van den Bergh
Duke Math. J. 122(3): 423-455 (15 April 2004). DOI: 10.1215/S0012-7094-04-12231-6

Abstract

For $Y,Y^+$ three-dimensional smooth varieties related by a flop, Bondal and Orlov conjectured that the derived categories $D^b({\rm coh}(Y))$ and $D^b({\rm coh}(Y^+))$ are equivalent. This conjecture was recently proved by Bridgeland. Our aim in this paper is to give a partially new proof of Bridgeland's result using noncommutative rings. The new proof also covers some mild singular and higher-dimensional situations (including those occuring in the recent paper by Chen [11]).

Citation

Download Citation

Michel Van den Bergh. "Three-dimensional flops and noncommutative rings." Duke Math. J. 122 (3) 423 - 455, 15 April 2004. https://doi.org/10.1215/S0012-7094-04-12231-6

Information

Published: 15 April 2004
First available in Project Euclid: 22 April 2004

zbMATH: 1074.14013
MathSciNet: MR2057015
Digital Object Identifier: 10.1215/S0012-7094-04-12231-6

Subjects:
Primary: 14E30 , 18E30
Secondary: 14A22

Rights: Copyright © 2004 Duke University Press

JOURNAL ARTICLE
33 PAGES

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

SHARE
Vol.122 • No. 3 • 15 April 2004
Back to Top