Groebner fan and embedded resolutions of ideals on toric varieties

2022/02/22 by Fuensanta Aroca, Aroca, Fuensanta, Mirna Gómez-Morales +3
Computer Science · Mathematics · #13F65 #14B05 #14M25 #14T90 #Algebraic Geometry (math.AG) #Algebraic Geometry and Number Theory #Commutative Algebra and Its Applications #FOS: Mathematics #Polynomial and algebraic computation

paper · pdf · doi:10.48550/arxiv.2202.10874

openalex publication_date 2022/02/22 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We consider the notions of Groebner fan and Newton non-degeneracy for an ideal on a toric variety, extending the two existing notions for ideals on affine spaces. We prove, without assumptions on the characteristic of the base fields, that the "Groebner fan" of such an ideal is actually a polyhedral fan and that a sub-variety defined by a Newton non-degenerate ideal on a toric variety X_σ admits a toric embedded resolution of singularities Z\longrightarrow X_σ.

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