On the Weights of Root Subgroups of Affine Toric Varieties

Immanuel van Santen

On the Weights of Root Subgroups of Affine Toric Varieties

Algebraic Geometry 2024-03-22 v1 Combinatorics

Authors: Immanuel van Santen

Abstract

Let $X$ be an affine toric variety and let $D(X)$ be the set of weights of all root subgroups. It is known that $D(X)$ together with its embedding into the character group determines $X$ as a toric variety. In this article we prove that $X$ is already determined by the abstract set $D(X)$ together with some additional combinatorial data.

Keywords

affine toric varieties root subgroups weights character group combinatorial data

Cite

@article{arxiv.2403.14389,
  title  = {On the Weights of Root Subgroups of Affine Toric Varieties},
  author = {Immanuel van Santen},
  journal= {arXiv preprint arXiv:2403.14389},
  year   = {2024}
}

Comments

22 pages, comments are welcome! The article arose of those parts of arXiv:2112.04784v1 that are not contained in arXiv:2112.04784v2. arXiv admin note: substantial text overlap with arXiv:2112.04784v1

On the Weights of Root Subgroups of Affine Toric Varieties

Abstract

Keywords

Cite

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