## Geometry & Topology

### Orbifold quantum Riemann–Roch, Lefschetz and Serre

Hsian-Hua Tseng

#### 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” 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.

#### Article information

Source
Geom. Topol., Volume 14, Number 1 (2010), 1-81.

Dates
Revised: 20 May 2009
Accepted: 22 June 2009
First available in Project Euclid: 20 December 2017

https://projecteuclid.org/euclid.gt/1513732171

Digital Object Identifier
doi:10.2140/gt.2010.14.1

Mathematical Reviews number (MathSciNet)
MR2578300

Zentralblatt MATH identifier
1178.14058

#### Citation

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

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