"Source: Text/Geometry/AlgSrf.text";
"Line: 996";
"Date: Thu Sep 25 14:47:45 2025";
"Main: Fri Sep 26 14:29:19 2025";
// original file: Text/Geometry/AlgSrf.text, line: 996
// Example: H126E4 ()
print "Example: H126E4";
ei := GetEchoInput();
SetEchoInput(true);
P<a,b,c,d,e,f> := ProjectiveSpace(Rationals(),5);
X := Surface(P,[b^2-a*c, a*d-b*f, b*d-c*f, d^2-c*e, a*e-f^2, b*e-d*f]);
// X is a Veronese surface, isomorphic to P^2
KodairaEnriquesType(X);
P<x,y,z,t> := ProjectiveSpace(Rationals(),3);
X := Surface(P,x^3*t+x^2*z^2-8*x*y^2*z-x*z*t^2+16*y^4+y^2*t^2-z^3*t);
KodairaEnriquesType(X);
P<x,y,z,t> := ProjectiveSpace(Rationals(),3);
X := Surface(P,x^6+2*x^5*y-2*x^4*y^2+2*x^2*y^4+y^6+x^4*t^2+2*x^3*y*t^2+
  x^2*y^2*t^2-x*y^3*t^2-2*y^4*t^2-x^2*y*t^3-2*x*y^2*t^3+2*x^2*t^4+y^2*t^4-
  z^2*t^4-x*t^5);
KodairaEnriquesType(X);
SetEchoInput(ei);
