Volume 10, issue 2 (2006)

Download this article
Download this article For screen
For printing
Recent Issues

Volume 28
Issue 7, 3001–3510
Issue 6, 2483–2999
Issue 5, 1995–2482
Issue 4, 1501–1993
Issue 3, 1005–1499
Issue 2, 497–1003
Issue 1, 1–496

Volume 27, 9 issues

Volume 26, 8 issues

Volume 25, 7 issues

Volume 24, 7 issues

Volume 23, 7 issues

Volume 22, 7 issues

Volume 21, 6 issues

Volume 20, 6 issues

Volume 19, 6 issues

Volume 18, 5 issues

Volume 17, 5 issues

Volume 16, 4 issues

Volume 15, 4 issues

Volume 14, 5 issues

Volume 13, 5 issues

Volume 12, 5 issues

Volume 11, 4 issues

Volume 10, 4 issues

Volume 9, 4 issues

Volume 8, 3 issues

Volume 7, 2 issues

Volume 6, 2 issues

Volume 5, 2 issues

Volume 4, 1 issue

Volume 3, 1 issue

Volume 2, 1 issue

Volume 1, 1 issue

The Journal
About the Journal
Editorial Board
Editorial Procedure
Subscriptions
 
Submission Guidelines
Submission Page
Policies for Authors
Ethics Statement
 
ISSN 1364-0380 (online)
ISSN 1465-3060 (print)
Author Index
To Appear
 
Other MSP Journals
Homogeneous coordinate rings and mirror symmetry for toric varieties

Mohammed Abouzaid

Geometry & Topology 10 (2006) 1097–1156

arXiv: math.SG/0511644

Abstract

Given a smooth toric variety X and an ample line bundle O(1), we construct a sequence of Lagrangian submanifolds of ()n with boundary on a level set of the Landau–Ginzburg mirror of X. The corresponding Floer homology groups form a graded algebra under the cup product which is canonically isomorphic to the homogeneous coordinate ring of X.

Keywords
homological mirror symmetry, toric varieties, tropical geometry
Mathematical Subject Classification 2000
Primary: 14J32
Secondary: 53D40
References
Forward citations
Publication
Received: 26 November 2005
Revised: 3 May 2006
Accepted: 1 June 2006
Published: 24 August 2006
Proposed: Jim Bryan
Seconded: Lothar Göttsche, Simon Donaldson
Authors
Mohammed Abouzaid
Department of Mathematics
University of Chicago
Chicago, IL 60637
USA