Measures of association between algebraic varieties

TL;DR

This paper explores measures of association between algebraic varieties, focusing on minimal complexity of correspondences, extending degree of irrationality results, and proposing conjectures and open problems.

Contribution

It introduces the concept of measures of association between algebraic varieties and extends existing results to this new setting.

Findings

Extended degree of irrationality results for hypersurfaces

Studied joint covering invariants for pairs of curves and hypersurfaces

Proposed several conjectures and open problems

Abstract

This paper begins the exploration of what we call measures of association between two irreducible complex projective varieties of the same dimension. The idea is to study from various points of view the minimal complexity of correspondences between them. We extend to this setting results about degrees of irrationality for hypersurfaces, and we study joint covering invariants for pairs of curves and hypersurfaces. We also propose a number of conjectures and open problems.