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

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On the Weights of Root Subgroups of Affine Toric Varieties

  • 期刊论文

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  • 发表日期：

    2025年1月14日

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  • Immanuel van Santen

摘要

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.