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arXiv · 2409.07986

Newton polyhedra and the integral closure of ideals on toric varieties

Amanda S. Araújo·Thaís M. Dalbelo·Thiago da Silva
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Abstract

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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Amanda S. Araújo, Thaís M. Dalbelo, Thiago da Silva. 2025-05-12. Newton polyhedra and the integral closure of ideals on toric varieties. https://arxiv.org/abs/2409.07986

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