Torsion order and irrationality of complete intersections

TL;DR

This paper establishes new lower bounds on the torsion order of general complete intersections and hypersurfaces, demonstrating their retract irrationality and advancing understanding of their algebraic complexity.

Contribution

It introduces novel logarithmic lower bounds for torsion order and proves the retract irrationality of certain algebraic varieties, extending previous results in algebraic geometry.

Findings

New logarithmic lower bounds for torsion order

Proof of retract irrationality for specific varieties

Advancement in understanding algebraic complexity of complete intersections

Abstract

We provide new logarithmic lower bounds for the torsion order of a very general complete intersection in projective space as well as a very general hypersurface in products of projective spaces and Grassmannians, in particular we prove their retract irrationality.