Coates, Tom; Gholampour, Amin; Iritani, Hiroshi; Jiang, Yunfeng; Johnson, Paul; Manolache, Cristina The quantum Lefschetz hyperplane principle can fail for positive orbifold hypersurfaces. (English) Zbl 1287.14027 Math. Res. Lett. 19, No. 5, 997-1005 (2012). In this article, the authors construct examples of a smooth orbifold \(X\) and a complete intersection \(Y\subset X\) determined by sections of vector bundles \(E=\oplus E_{j}\rightarrow X\) such that \(E_{j}\) is a line bundle with \(c_{1}(E_{j})\cdot d \geq 0\), whenever \(d\) is the degree of genus 0 stable map to \(X\), but there is no cohomology class \(e\) on \(X_{0,n,d}\)(moduli stack of degree d stable maps to \(X\) from genus 0 curves with \(n\) marked points) with \(\sum_{\delta:i_{*}\delta=d}i_{*}[Y_{0,n,\delta}]^{vir}=[X_{0,n,d}]^{vir} \cap e.\) In other words, the quantum Lefschetz hyperplane principle can fail for positive orbifold complete intersections. Reviewer: Vehbi Emrah Paksoy (Fort Lauderdale) Cited in 11 Documents MSC: 14N35 Gromov-Witten invariants, quantum cohomology, Gopakumar-Vafa invariants, Donaldson-Thomas invariants (algebro-geometric aspects) 53D45 Gromov-Witten invariants, quantum cohomology, Frobenius manifolds 14D23 Stacks and moduli problems Keywords:Gromov-Witten invariants; orbifolds; quantum cohomology; hypersurfaces; complete intersections; quantum Lefschetz hyperplane theorem PDFBibTeX XMLCite \textit{T. Coates} et al., Math. Res. Lett. 19, No. 5, 997--1005 (2012; Zbl 1287.14027) Full Text: DOI arXiv