A semigroup defining the Gr\"obner degeneration of a toric ideal
Hern\'an de Alba Casillas, Daniel Duarte, Ra\'ul Vargas Antuna
TL;DR
This paper provides an explicit generating set for the semigroup associated with the Gr"obner degeneration of a toric ideal, enabling detailed analysis of its algebraic properties and structural features.
Contribution
It introduces a specific set of generators for the semigroup, facilitating the study of various algebraic and combinatorial properties of the Gr"obner degeneration.
Findings
Explicit generators for the semigroup are constructed.
The semigroup's approximation and saturation properties are analyzed.
The study reveals the behavior of Betti elements and presentation uniqueness.
Abstract
We give an explicit set of generators for the semigroup of the Gr\"obner degeneration of a toric ideal. This set of generators is used to study algebraic properties of the semigroup it generates: approximation of semigroups, non-preservation of saturation, Betti elements, uniqueness of presentations, and M\"obius functions.
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Taxonomy
TopicsCommutative Algebra and Its Applications