Counterexamples of Lefschetz hyperplane type results for movable cones

TL;DR

This paper constructs counterexamples demonstrating that the movable cone of an ample divisor can differ from that of its ambient variety, challenging existing assumptions in algebraic geometry.

Contribution

It introduces a method to produce explicit counterexamples where the Lefschetz hyperplane type results fail for movable cones.

Findings

Counterexamples show the discrepancy between movable cones of divisors and ambient varieties.

The main theorem provides a systematic way to generate such counterexamples.

Results impact the understanding of cone behavior in algebraic geometry.

Abstract

The main theorem of the paper provides a way to produce examples such that the movable cone of an ample divisor does not coincide with the movable cone of its ambient variety.