Multiplicative bounds for measures of irrationality on complete intersections

TL;DR

This paper proves that measures of irrationality for certain complete intersections are multiplicative in the degrees of their defining equations, confirming parts of a conjecture and advancing understanding of their geometric properties.

Contribution

It establishes the multiplicativity of irrationality measures for very general complete intersections, confirming specific cases of a conjecture in algebraic geometry.

Findings

Measures of irrationality are multiplicative for certain complete intersections.

Confirms cases of a conjecture by Bastianelli et al.

Uses numerical invariants of curves to analyze irrationality.

Abstract

We show that measures of irrationality on very general codimension two complete intersections and very general complete intersection surfaces are multiplicative in the degrees of the defining equations. This confirms some cases of a conjecture of Bastianelli, De Poi, Ein, Lazarsfeld, and Ullery. Our methods involve studying the numerical invariants of curves on complete intersections.