Skip Navigation

International Mathematics Research Papers (2006) Vol. 2006 : article ID 69590, 116 pages, doi:10.1155/IMRP/2006/69590
This Article
Right arrow Full Text (PDF)
Right arrow References
Right arrow Alert me when this article is cited
Right arrow Alert me if a correction is posted
Services
Right arrow Email this article to a friend
Right arrow Similar articles in this journal
Right arrow Alert me to new issues of the journal
Right arrow Add to My Personal Archive
Right arrow Download to citation manager
Right arrowRequest Permissions
Right arrow How to cite this article
Google Scholar
Right arrow Articles by Khoroshkin, S.
Right arrow Articles by Varchenko, A.
Right arrow Search for Related Content
Social Bookmarking
Add to CiteULike   Add to Connotea   Add to Del.icio.us  
What's this?

Copyright © 2006 Hindawi Publishing Corporation. All rights reserved.

Quiver D-modules and homology of local systems over an arrangement of hyperplanes

S. Khoroshkin and A. Varchenko

Institute for Theoretical and Experimental Physics Moscow 117259, Russia E-mail address: khor{at}itep.ru
Department of Mathematics, University of North Carolina at Chapel Hill NC 27599-3250, USA E-mail address: anv{at}email.unc.edu

Let C be an arrangement of hyperplanes in CN, D the ring of algebraic differential operators on CN. We define a category of quivers associated with C. A quiver is a collection of vector spaces, attached to strata of the arrangement, and suitable linear maps between the spaces . To a quiver we assign a D-module on CN, called a quiver D-module. We describe basic operations for D-modules in terms of linear algebra of quivers. We give an explicit construction of a free resolution of a quiver D-module and use the construction to describe the associated perverse sheaf. As an application, we calculate the cohomology of CN with coefficients in the quiver perverse sheaf (under certain assumptions).


Add to CiteULike CiteULike   Add to Connotea Connotea   Add to Del.icio.us Del.icio.us    What's this?




Disclaimer: Please note that abstracts for content published before 1996 were created through digital scanning and may therefore not exactly replicate the text of the original print issues. All efforts have been made to ensure accuracy, but the Publisher will not be held responsible for any remaining inaccuracies. If you require any further clarification, please contact our Customer Services Department.