Equations for the Fifth Secant Variety of Segre Products of Projective Spaces

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.”

Keywords:

• 2000 AMS Subject Classification: 14M07
• 14Q15
• 15A69
• secant variety
• equations
• young symmetrizers
• binary tensors
• tensor mark

Notes

¹Our methods include probabilistic symbolic computations and numerical computations. Though they have been carefully tested and produce completely reproducible results, they are technically only true with high probability, or up to the numerical precision of the computers we use. To indicate reliance on such computations, we designate those theorems, corollaries, and propositions with a star.

²One with 24 cores 2.8 GHz Intel Xeon processors with 144 GB RAM and another with 40 cores 2.8 GHz Intel Xeon processors with 256GB of RAM.