Curves on quartics

1860 days ago by jakub.witaszek

P3 = ProjectiveSpace(3, QQ, 'x') P3.inject_variables() r=1 #parameter of bicuspid curve f = (x0^2-x2^2*r^2)*(x0-x2*r)^2 + (x1^2-x2^2*r^2)^2 #bicuspidal curve a=1 b=3 c=7 X = P3.subscheme(f + x3*(a*x0^3+b*x1^3+c*x2^3) + x3^4) 
       
Defining x0, x1, x2, x3
X.is_smooth() 
       
True