Search arXiv⌕ Search
Home/Archive/arXiv

arXiv · 2310.06477

Newton-Okounkov polytopes of type $A$ flag varieties of small ranks arising from cluster structures

Yunhyung Cho·Naoki Fujita·Akihiro Higashitani·Eunjeong Lee
View original source ↗Read source document ↗Export metadata ↓

Abstract

A flag variety is a smooth projective homogeneous variety. In this paper, we study Newton-Okounkov polytopes of the flag variety $Fl(\mathbb{C}^4)$ arising from its cluster structure. More precisely, we present defining inequalities of such Newton-Okounkov polytopes of $Fl(\mathbb{C}^4)$. Moreover, we classify these polytopes, establishing their equivalence under unimodular transformations.

Explore related subjects

math.AGmath.COmath.RT

Keep this discovery

Explore connections, maps & timelines

BibTeXRIS

Yunhyung Cho, Naoki Fujita, Akihiro Higashitani, Eunjeong Lee. 2023-10-10. Newton-Okounkov polytopes of type $A$ flag varieties of small ranks arising from cluster structures. https://arxiv.org/abs/2310.06477

Cite the original work for its findings. Save a collection to share your selection of sources.

KEEP EXPLORING

Related papers

arXiv2026

G3-Criteria and Applications

The G3-property of a subvariety was introduced by Hironaka-Matsumura, and plays an important role for deducing connectedness and extension results. Unfortunately, it's a rather elusive notion, which is not always easy to establish. Most of the existing work is concentrated on subvarieties of homogeneous varieties. The first goal of this article is to show that mobility assumptions on the subvariety, considered in works of Badescu, Chow, Debarre, Voisin, yield a certain partial positivity property, slightly stronger than G3, previously introduced by the author. Second, we apply the result to prove that, in numerous situations, the splitting of the normal bundle of a smooth two-codimensional subvariety implies that it is a complete intersection.

math.AG↗
arXiv2026

Nodal degeneration of chiral algebras I: Global structure and gluing formula

We define a natural extension of a universal factorization algebra $\mathcal{A}$ to families of stable punctured curves, by integrating over all semistable modifications. We prove that the resulting sheaf of factorization homology satisfies a natural gluing formula, by tensoring over a certain derived associative algebra $\mathfrak{Z}_{\mathcal{A}}^0$, generalizing the Verlinde formula for gluing of conformal blocks.

math.AG↗