Orbifold Quantum Riemann-Roch, Lefschetz and Serre

Details Orbifold Quantum Riemann-Roch, Lefschetz and Serre Orbifold Quantum Riemann-Roch, Lefschetz and Serre

2005-06-07

arxiv.org/abs/math/0506111v4

Geometry and Topology 14 (2010) 1--81

Mathematics

Algebraic Geometry

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

Scientific paper

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.

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