Mathematical Research Letters

Volume 19 (2012)

Number 5

The quantum Lefschetz hyperplane principle can fail for positive orbifold hypersurfaces

Pages: 997 – 1005



Tom Coates (Department of Mathematics, Imperial College London)

Amin Gholampour (Department of Mathematics, University of Maryland)

Hiroshi Iritani (Department of Mathematics, Graduate School of Science, Kyoto University, Japan)

Yunfeng Jiang (Department of Mathematics, Imperial College London)

Paul Johnson (Mathematics Department, Columbia University, New York, N.Y.)

Cristina Manolache (Institut für Mathematik, Humboldt Universität, Berlin, Germany)


We show that the Quantum Lefschetz Hyperplane Principle can fail for certain orbifold hypersurfaces and complete intersections. It can fail even for orbifold hypersurfaces defined by a section of an ample line bundle.


Gromov–Witten invariants, orbifolds, quantum cohomology, hypersurfaces, complete intersections, Quantum Lefschetz Hyperplane Theorem

Published 15 March 2013