Bounding the degrees of a minimal μ-basis for a rational surface parametrization

2016/11/22 by Cid-Ruiz, Yairon
#Commutative Algebra (math.AC) #FOS: Mathematics

paper · doi:10.48550/arxiv.1611.07506

Abstract

In this paper, we study how the degrees of the elements in a minimal μ-basis of a parametrized surface behave. For an arbitrary rational surface parametrization P(s,t)=(a₁(s,t),a₂(s,t),a₃(s,t),a₄(s,t)) ∈ \mathbbF[s,t]⁴ over an infinite field \mathbbF, we show the existence of a μ-basis with polynomials bounded in degree by O(d³³), where d=max(deg(a₁),deg(a₂), deg(a₃), deg(a₄)). Under additional assumptions we can obtain tighter bounds.

Related

• The parametric degree of a rational surface
• Implicitization of rational ruled surfaces with μ-bases
• Minimal solutions of the rational interpolation problem
• Covering Rational Ruled Surfaces
• On the structure of mu-classes