Double Schubert polynomials do have saturated Newton polytopes
Commutative Algebra
2023-10-10 v3 Algebraic Geometry
Combinatorics
Abstract
We prove that double Schubert polynomials have the Saturated Newton Polytope property. This settles a conjecture by Monical, Tokcan and Yong. Our ideas are motivated by the theory of multidegrees. We introduce a notion of standardization of ideals that enables us to study non-standard multigradings. This allows us to show that the support of the multidegree polynomial of each Cohen-Macaulay prime ideal, and in particular, that of each Schubert determinantal ideal is a discrete polymatroid.
Cite
@article{arxiv.2109.10299,
title = {Double Schubert polynomials do have saturated Newton polytopes},
author = {Federico Castillo and Yairon Cid-Ruiz and Fatemeh Mohammadi and Jonathan Montaño},
journal= {arXiv preprint arXiv:2109.10299},
year = {2023}
}
Comments
to appear in Forum of Mathematics, Sigma