|
|||||
|
|
|
|
|
|
|
|
|
Orbifold quantum
Riemann–Roch, Lefschetz and Serre
Hsian-Hua Tseng |
|
Geometry & Topology 14 (2010) 1–81
|
|
DOI: 10.2140/gt.2010.14.1
|
Abstract |
|
Given a vector bundle on a smooth Deligne–Mumford stack and an invertible multiplicative characteristic class , we define orbifold Gromov–Witten invariants of twisted by and . 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– orbifold Gromov–Witten invariants of 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 |
|
