Newton-Okounkov bodies of flag varieties and combinatorial mutations
Abstract
A Newton-Okounkov body is a convex body constructed from a projective variety with a globally generated line bundle and with a higher rank valuation on the function field, which gives a systematic method of constructing toric degenerations of projective varieties. Its combinatorial properties heavily depend on the choice of a valuation, and it is a fundamental problem to relate Newton-Okounkov bodies associated with different kinds of valuations. In this paper, we address this problem for flag varieties using the framework of combinatorial mutations which was introduced in the context of mirror symmetry for Fano manifolds. By applying iterated combinatorial mutations, we connect specific Newton-Okounkov bodies of flag varieties including string polytopes, Nakashima-Zelevinsky polytopes, and FFLV polytopes.
Keywords
Cite
@article{arxiv.2003.10837,
title = {Newton-Okounkov bodies of flag varieties and combinatorial mutations},
author = {Naoki Fujita and Akihiro Higashitani},
journal= {arXiv preprint arXiv:2003.10837},
year = {2025}
}
Comments
v1: 22 pages. v2: 25 pages. The organization of the paper has been changed. The main results are unchanged. To appear in Int. Math. Res. Not. arXiv admin note: text overlap with arXiv:2002.09912