On the multiplicity and regularity index of toric curves
Daniel Duarte, Alondra Ram\'irez Sandoval
TL;DR
This paper investigates the combinatorial aspects of the multiplicity at the origin of toric curves and provides exact and bounded values for the regularity index, enhancing understanding of their algebraic and geometric properties.
Contribution
It offers a combinatorial method to determine the multiplicity and exact and bounded values for the regularity index of toric curves at the origin.
Findings
Exact regularity index for plane toric curves.
Effective bounds for the regularity index of arbitrary toric curves.
A combinatorial approach to multiplicity at the origin.
Abstract
In this note we revisit the problem of determining combinatorially the multiplicity at the origin of a toric curve. In addition, we give the exact value of the regularity index of that point for plane toric curves and effective bounds for this number for arbitrary toric curves.
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Taxonomy
TopicsCommutative Algebra and Its Applications · Algebraic Geometry and Number Theory · Advanced Numerical Analysis Techniques