Double Schubert polynomials do have saturated Newton polytopes
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 nonstandard multigradings....
| Hlavní autoři: | , , , |
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| Médium: | Článek |
| Jazyk: | English |
| Vydáno: |
Cambridge University Press
2023-01-01
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| Edice: | Forum of Mathematics, Sigma |
| Témata: | |
| On-line přístup: | https://www.cambridge.org/core/product/identifier/S2050509423001019/type/journal_article |
| Shrnutí: | 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 nonstandard multigradings. This allows us to show that the support of the multidegree polynomial of each Cohen–Macaulay prime ideal in a nonstandard multigrading, and in particular, that of each Schubert determinantal ideal is a discrete polymatroid. |
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| ISSN: | 2050-5094 |