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 $\bc$, we define the orbifold Gromov-Witten invariants of $\X$ twisted by $F$ and $\bc$. 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. This provides a way to verify mirror symmetry predictions for complete intersection orbifolds.

major revision: numerous changes made, mistakes corrected, some new materials added

References in corpus (5)

• Computing Genus-Zero Twisted Gromov-Witten Invariants
• Wall-Crossings in Toric Gromov-Witten Theory I: Crepant Examples
• Pointed Admissible G-Covers and G-equivariant Cohomological Field Theories
• String topology for stacks
• On computations of Hurwitz-Hodge integrals

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