源于簇结构的 Schubert 簇的 Newton-Okounkov 多面体
表示论
2025-07-25 v3 代数几何
组合数学
摘要
Newton-Okounkov 体的理论是环面簇 Newton 多面体理论的推广，它给出了构造射影簇环面退化的系统方法。本文从簇代数理论出发研究 Schubert 簇的 Newton-Okounkov 体。我们利用推广簇理论中扩展 g-向量的特定赋值构造 Newton-Okounkov 体，并讨论这些体与字符串多面体及 Nakashima-Zelevinsky 多面体的关系。
引用
@article{arxiv.2002.09912,
title = {Newton-Okounkov polytopes of Schubert varieties arising from cluster structures},
author = {Naoki Fujita and Hironori Oya},
journal= {arXiv preprint arXiv:2002.09912},
year = {2025}
}
备注
v1 55 pages; v2 57 pages. Section 7 in v1 was removed, and the corresponding results are explained in Sections 5 and 6 in v2, since the statement of Theorem 7.5 in v1 is now known to be true in the symmetrizable case. Section 7 in v2 was added; v3 60 pages. Remark 8.5, Proposition 8.6 and several examples were added. Minor typos were corrected. Final version