The Quantum Lefschetz Hyperplane Principle Can Fail for Positive Orbifold Hypersurfaces

TL;DR

This paper demonstrates that the Quantum Lefschetz Hyperplane Principle, a key tool in algebraic geometry, can fail in the context of orbifold hypersurfaces, even when these are defined by ample line bundles.

Contribution

It provides the first known examples where the Quantum Lefschetz Hyperplane Principle does not hold for orbifold hypersurfaces, challenging previous assumptions.

Findings

Quantum Lefschetz can fail for orbifold hypersurfaces

Failure occurs even with ample line bundle sections

Highlights limitations of the principle in orbifold settings

Abstract

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.