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))∈F[s,t]4 over an infinite field F, 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.
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