Normal Toric Ideals of Low Codimension
Pierre Dueck, Serkan Hosten, Bernd Sturmfels
TL;DR
This paper proves that all normal toric ideals of codimension two have a specific minimal generating set and provides an efficient algorithm to verify normality for fixed codimension toric ideals.
Contribution
It establishes a structural property of normal toric ideals of codimension two and introduces a polynomial-time algorithm for checking normality in fixed codimension cases.
Findings
Normal toric ideals of codimension two are generated by a Grobner basis with squarefree initial monomials.
A polynomial-time algorithm is developed for testing normality of fixed codimension toric ideals.
The results connect the algebraic structure of toric ideals with computational methods.
Abstract
Every normal toric ideal of codimension two is minimally generated by a Grobner basis with squarefree initial monomials. A polynomial time algorithm is presented for checking whether a toric ideal of fixed codimension is normal.
Peer Reviews
No public reviews on file for this paper yet. If you reviewed it on a platform where reviews are public (OpenReview, ICLR, NeurIPS, ICML), you can paste yours below so the community can read it here.
Videos
No videos yet. Explain this paper in a talk, walkthrough, or lecture? Add one.
Taxonomy
TopicsCommutative Algebra and Its Applications · Polynomial and algebraic computation · Algebraic Geometry and Number Theory