Geometry & Topology 14 (2010) 1–81

DOI: 10.2140/gt.2010.14.1

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

Primary: 14N35

Secondary: 14C40, 53D45

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