TOTAL DEGREE FORMULA FOR THE GENERIC OFFSET TO A PARAMETRIC SURFACE

Given a surface parametrization (non-necessarily birational) we provide a formula for computing the total degree of its generic offset. The formula essentially uses gcds and resultants of polynomials directly obtained from the input parametrization. In addition, it must be said that the formula is valid under the conjecture that not all offsets to a fixed rational (algebraic) surface pass though a fixed point; this was proved to be true in the curve case [Degree formulae for offset curves, J. Pure Appl. Algebra195(3) (2005) 301–335].