Rational Complexity-One T-Varieties Are Well-Poised

Nathan Ilten, Christopher Manon

Research output: Contribution to journalReview articlepeer-review

9 Scopus citations


Given an affine rational complexity-one T-variety X, we construct an explicit embedding of X in affine space An. We show that this embedding is well-poised, that is, every initial ideal of IX is a prime ideal, and we determine the tropicalization Trop(X). We then study valuations of the coordinate ring RX of X which respect the torus action, showing that for full rank valuations, the natural generators of RX form a Khovanskii basis. This allows us to determine Newton-Okounkov bodies of rational projective complexity-one T-varieties, partially recovering (and generalizing) results of Petersen. We apply our results to describe all integral special fibres of K* × T-equivariant degenerations of rational projective complexity-one T-varieties, generalizing a result of Süß and Ilten.

Original languageEnglish
Pages (from-to)4198-4232
Number of pages35
JournalInternational Mathematics Research Notices
Issue number13
StatePublished - Jul 1 2019

Bibliographical note

Publisher Copyright:
© 2017 The Author(s). Published by Oxford University Press. All rights reserved.

ASJC Scopus subject areas

  • General Mathematics


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