Geometry & Topology
- Geom. Topol.
- Volume 14, Number 1 (2010), 1-81.
Orbifold quantum Riemann–Roch, Lefschetz and Serre
Given a vector bundle on a smooth Deligne–Mumford stack and an invertible multiplicative characteristic class , we define orbifold Gromov–Witten invariants of twisted by and . 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– orbifold Gromov–Witten invariants of and that of a complete intersection, under additional assumptions. This provides a way to verify mirror symmetry predictions for some complete intersection orbifolds.
Geom. Topol., Volume 14, Number 1 (2010), 1-81.
Received: 16 July 2006
Revised: 20 May 2009
Accepted: 22 June 2009
First available in Project Euclid: 20 December 2017
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Mathematical Reviews number (MathSciNet)
Zentralblatt MATH identifier
Primary: 14N35: Gromov-Witten invariants, quantum cohomology, Gopakumar-Vafa invariants, Donaldson-Thomas invariants [See also 53D45]
Secondary: 53D45: Gromov-Witten invariants, quantum cohomology, Frobenius manifolds [See also 14N35] 14C40: Riemann-Roch theorems [See also 19E20, 19L10]
Tseng, Hsian-Hua. Orbifold quantum Riemann–Roch, Lefschetz and Serre. Geom. Topol. 14 (2010), no. 1, 1--81. doi:10.2140/gt.2010.14.1. https://projecteuclid.org/euclid.gt/1513732171