Volume 14, issue 1 (2010)

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

Volume 28
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
Orbifold quantum Riemann–Roch, Lefschetz and Serre

Hsian-Hua Tseng

Geometry & Topology 14 (2010) 1–81
Abstract

Given a vector bundle F on a smooth Deligne–Mumford stack X and an invertible multiplicative characteristic class c, we define orbifold Gromov–Witten invariants of X twisted by F and c. We prove a “quantum Riemann–Roch theorem” which expresses the generating function of the twisted invariants in terms of the generating function of the untwisted invariants. A quantum Lefschetz hyperplane theorem is derived from this by specializing to genus zero. As an application, we determine the relationship between genus–0 orbifold Gromov–Witten invariants of X and that of a complete intersection, under additional assumptions. This provides a way to verify mirror symmetry predictions for some complete intersection orbifolds.

Keywords
orbifold Gromov–Witten invariant, Deligne–Mumford stack, Givental's formalism, Grothendieck–Riemann–Roch formula, mirror symmetry
Mathematical Subject Classification 2000
Primary: 14N35
Secondary: 53D45, 14C40
References
Publication
Received: 16 July 2006
Revised: 20 May 2009
Accepted: 22 June 2009
Preview posted: 10 October 2009
Published: 2 January 2010
Proposed: Jim Bryan
Seconded: Richard Thomas, Frances Kirwan
Authors
Hsian-Hua Tseng
Department of Mathematics
Ohio State University
100 Math Tower
231 West 18th Avenue
Columbus, OH 43210-1174
USA
Department of Mathematics
University of Wisconsin-Madison
Van Vleck Hall
480 Lincoln Drive
Madison, WI 53706-1388
USA