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arXiv · 2109.10299

Double Schubert polynomials do have saturated Newton polytopes

Federico Castillo·Yairon Cid-Ruiz·Fatemeh Mohammadi·Jonathan Montaño
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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.

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Federico Castillo, Yairon Cid-Ruiz, Fatemeh Mohammadi, Jonathan Montaño. 2021-09-21. Double Schubert polynomials do have saturated Newton polytopes. https://arxiv.org/abs/2109.10299

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