Volume 13, issue 5 (2009)

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

Volume 20
Issue 4, 1807–2438
Issue 3, 1257–1806
Issue 2, 629–1255
Issue 1, 1–627

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 Interests
Editorial Procedure
Submission Guidelines
Submission Page
Subscriptions
Author Index
To Appear
Contacts
ISSN (electronic): 1364-0380
ISSN (print): 1465-3060
Wall-crossings in toric {G}romov–{W}itten theory {I}: crepant examples

Tom Coates, Hiroshi Iritani and Hsian-Hua Tseng

Geometry & Topology 13 (2009) 2675–2744
Abstract

Let X be a Gorenstein orbifold with projective coarse moduli space X and let Y be a crepant resolution of X. We state a conjecture relating the genus-zero Gromov–Witten invariants of X to those of Y , which differs in general from the Crepant Resolution Conjectures of Ruan and Bryan–Graber, and prove our conjecture when X = (1,1,2) and X = (1,1,1,3). As a consequence, we see that the original form of the Bryan–Graber Conjecture holds for (1,1,2) but is probably false for (1,1,1,3). Our methods are based on mirror symmetry for toric orbifolds.

Keywords
quantum cohomology, crepant resolution, Gromov–Witten invariants, mirror symmetry, variation of semi-infinite Hodge structure, Crepant Resolution Conjecture
Mathematical Subject Classification 2000
Primary: 53D45
Secondary: 14N35, 83E30
References
Publication
Received: 4 December 2006
Revised: 21 October 2008
Accepted: 25 May 2009
Published: 2 August 2009
Proposed: Jim Bryan
Seconded: Richard Thomas, Lothar Goettsche
Authors
Tom Coates
Department of Mathematics
Imperial College London
180 Queen’s Gate
London SW7 2AZ
UK
Hiroshi Iritani
Faculty of Mathematics
Kyushu University
6-10-1, Hakozaki
Higashiku, Fukuoka, 812-8581
Japan
Hsian-Hua Tseng
Department of Mathematics
University of Wisconsin–Madison
Van Vleck Hall, 480 Lincoln Drive
Madison, WI 53706-1388
USA