Short polynomials in determinantal ideals

Abstract

We show that a determinantal ideal generated by $t$-minors does not contain any nonzero polynomials with $t!/2$ or fewer terms. Geometrically this means that any nonzero polynomial vanishing on all matrices of rank at most $t-1$ has more than $t!/2$ terms.

8 pages. Comments welcome

Cited by in corpus (1)

• Ideals, Determinants, and Straightening: Proving and Using Lower Bounds for Polynomial Ideals