Bounding the degrees of a minimal μ-basis for a rational surface parametrization. (November 2019) - Cid-Ruiz, Yairon
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 ) = ( a 1 ( s, t ), a 2 ( s, t ), a 3 ( s, t ), a 4 ( 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 ( d 33 ), where d = max ⁡ ( deg ⁡ ( a 1 ), deg ⁡ ( a 2 ), deg ⁡ ( a 3 ), deg ⁡ ( a 4 ) ) . Under additional assumptions we can obtain tighter bounds.