Equations for the fifth secant variety of Segre products of projective spaces

TL;DR

This paper provides a computational proof that the fifth secant variety of a specific Segre product is a codimension 2 complete intersection, using probabilistic methods with high numerical accuracy.

Contribution

It offers the first computational proof of the defining equations for this secant variety, employing pseudo-randomness and numerical techniques.

Findings

The fifth secant variety is a codimension 2 complete intersection.

The defining equations have degrees 6 and 16.

The proof relies on probabilistic computational methods.

Abstract

We describe a computational proof that the fifth secant variety of the Segre product of five copies of the projective line is a codimension 2 complete intersection of equations of degree 6 and 16. Our computations rely on pseudo-randomness, and numerical accuracy, so parts of our proof are only valid "with high probability".