Orbifold quantum Riemann-Roch, Lefschetz and Serre

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" (Theorem 4.2.1) 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.