Parametric equations of plane sextic curves with a maximal set of double points

Abstract

We give explicit parametric equations for all irreducible plane projective sextic curves which have at most double points and whose total Milnor number is maximal (is equal to 19). In each case we find a parametrization over a number field of the minimal possible degree and try to choose coordinates so that the coefficients are as small as we can do.

12 pages. v2: Misprints in the definitions of the curves no.10 and 12 are corrected. The file sextics-param.txt with the equations in the maple format is added to the arxiv submission