Archived

This content is available here for research, reference, and/or recordkeeping.

Abstract

An embedded variety is said to be well-poised when the associated initial ideal degenerations coming from points of the tropical variety are reduced and irreducible. Varieties with a well-poised embedding admit a large collection of explicitly constructible Newton-Okounkov bodies. This paper aims to study the well-poised property under torus quotients. Our first result states that GIT quotients of normal well-poised varieties by quasi-tori also have well-poised embeddings. As an application, we show that several Hassett spaces, (Formula presented.), are well-poised under Alexeev’s embedding. Conversely, given an affine T-variety X with polyhedral divisor (Formula presented.) on a well-poised base Y, we construct an embedding of (Formula presented.) and provide conditions on Y and (Formula presented.) which if met, imply X is well-poised under this embedding. Then we show that any affine arrangement variety meets the specified criteria, generalizing results of Ilten and the second author for rational complexity 1 varieties. Using this result, we explicitly compute many Newton-Okounkov cones of X and provide a criterion for the associated toric degenerations to be normal. Our final application combines these two results to show that hypertoric varieties have well-poised embeddings.

Document Type

Article

Publication Date

1-1-2026

Notes/Citation Information

Publisher Copyright: © 2026 Taylor & Francis Group, LLC.

Digital Object Identifier (DOI)

10.1080/00927872.2026.2636238

Archival?

Archival

Download

Share

COinS