Converting subalgebra bases with the Sagbi walk

Converting Bases with the Gröbner Walk

The objective of this note is the presentation of a procedure for converting a given Gröbner basis (Buchberger, 1965) of a polynomial ideal I to a Gröbner basis of I with respect to another term order. This procedure, which we call the Gröbner walk, is completely elementary and does not require any assumptions about the dimension or the number of variables of the ideal. The Gröbner walk breaks ...

SAGBI Bases Under Composition

Our interest in the subject of this paper is inspired by Hong (1998), where Hoon Hong addresses the problem of the behavior of Gröbner bases under composition of polynomials. More precisely, let Θ be a set of polynomials, as many as the variables in our polynomial ring. The question then is under which conditions on these polynomials it is true that for an arbitrary Gröbner basis G (with respec...

SAGBI and SAGBI-Gröbner Bases over Principal Ideal Domains

On the (De)homogenization of Sagbi Bases

In this paper we study the relation between nonhomogeneous and homogeneous Sagbi bases. As a consequence, we present a general principle of computing Sagbi bases of a subalgebra and its homogenized subalgebra, which is based on passing over to homogenized generators.

Sagbi Bases of Cox-Nagata Rings

We degenerate Cox–Nagata rings to toric algebras by means of sagbi bases induced by configurations over the rational function field. For del Pezzo surfaces, this degeneration implies the Batyrev–Popov conjecture that these rings are presented by ideals of quadrics. For the blow-up of projective n-space at n + 3 points, sagbi bases of Cox–Nagata rings establish a link between the Verlinde formul...