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Orbifold quantum Riemann-Roch, Lefschetz and Serre. (English) Zbl 1178.14058
The author aims to extend the quantum Riemann-Roch theorem given by Coates and Givental in Gromov-Witten theory to smooth Deligne-Mumford stacks. The orbifold GW invariants of a smooth Deligne-Mumford stack is defined. A quantum Lefschetz hyperplane theorem is also derived. In this paper, one can also find the relations between genus 0 GW invariants of Deligne-Mumford stacks and that of a complete intersection, with additional assumptions.

MSC:
14N35 Gromov-Witten invariants, quantum cohomology, Gopakumar-Vafa invariants, Donaldson-Thomas invariants (algebro-geometric aspects)
14C40 Riemann-Roch theorems
53D45 Gromov-Witten invariants, quantum cohomology, Frobenius manifolds
14D23 Stacks and moduli problems
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