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....
| المؤلفون الرئيسيون: | , , , |
|---|---|
| التنسيق: | مقال |
| اللغة: | English |
| منشور في: |
Cambridge University Press
2023-01-01
|
| سلاسل: | Forum of Mathematics, Sigma |
| الموضوعات: | |
| الوصول للمادة أونلاين: | https://www.cambridge.org/core/product/identifier/S2050509423001019/type/journal_article |
| الملخص: | 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. |
|---|---|
| تدمد: | 2050-5094 |