Stabilized measures of association: comparing the birational geometry of varieties having different dimensions

TL;DR

This paper introduces new invariants to compare the birational geometry of varieties with different dimensions, extending existing measures of association for broader applicability.

Contribution

It develops and explores invariants that enable comparison of birational geometries across varieties of differing dimensions, with practical examples and computations.

Findings

New invariants for comparing birational geometries

Examples illustrating the invariants' application

Computed invariants in specific cases of interest

Abstract

We extend some of the measures of association defined by Lazarsfeld and Martin, obtaining useful invariants to compare the birational geometry of two varieties having different dimensions. We explore such invariants providing examples and computing them in some cases of interest.