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On the Weights of Root Subgroups of Affine Toric Varieties | Synapse

February 26, 20260 citationsOpen Access

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On the Weights of Root Subgroups of Affine Toric Varieties

ISImmanuel van SantenUniversity of Basel

Key Points

To prove that the abstract set of weights of root subgroups is sufficient to determine an affine toric variety.
Analyzed the set of weights D(X) of root subgroups.
Examined its relationship with the character group.
Introduced additional combinatorial data for characterization.
Established that D(X) alone can determine the structure of the toric variety X.
Showed that embedding into the character group is not always necessary.

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.

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Cite This Study

Immanuel van Santen (Wed,) studied this question.

synapsesocial.com/papers/699f95951bc9fecf3dab3907 https://doi.org/https://doi.org/10.48620/93282