牛顿多面体与环状变体上理想的积分闭合

Amanda S. Araújo, Thaís M. Dalbelo, Thiago da Silva
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引用次数: 0

摘要

在这项工作中,我们将萨伊亚关于牛顿非退化理想的表征的结果扩展到$O_{X(S)}$中的理想,其中$X(S)$是由半群$S\subset \mathbb{Z}^{n}_{+}$定义的仿射环综。我们引入并描述了非退化理想,证明它们的积分闭包是由与牛顿多面体相关的特定单项式生成的。
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Newton polyhedra and the integral closure of ideals on toric varieties
In this work, we extend Saia's results on the characterization of Newton non-degenerate ideals to the context of ideals in $O_{X(S)}$, where $X(S)$ is an affine toric variety defined by the semigroup $S\subset \mathbb{Z}^{n}_{+}$. We explore the relationship between the integral closure of ideals and the Newton polyhedron. We introduce and characterize non-degenerate ideals, showing that their integral closure is generated by specific monomials related to the Newton polyhedron.
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