Slicing Correspondences with High Degree Hypersurfaces

TL;DR

This paper introduces a method to approximate the correspondence degree between unbalanced complete intersections by analyzing subvarieties of product spaces, revealing a bijection that could have broader implications.

Contribution

It provides a novel approach to approximate correspondence degrees using intersection techniques on product varieties, establishing a new bijection.

Findings

Approximate computation of correspondence degree for unbalanced complete intersections.

Establishment of a bijection between certain sets of varieties via intersection methods.

Potential implications for understanding correspondences in algebraic geometry.

Abstract

We approximately compute the correspondence degree (as defined by Lazarsfeld and Martin) between two unbalanced complete intersections. This is accomplished by showing that the procedure of taking a subvariety of a product $Y \times Y'$ and intersecting it with $X \times Y'$ (for $X$ a sufficiently ample smooth divisor in $Y$) induces a bijection between two sets of varieties. This may be of independent interest.