Kummer surfaces over a general ring#
- class sage.schemes.hyperelliptic_curves.kummer_surface.KummerSurface(J)[source]#
Bases:
AlgebraicScheme_subscheme_projective
EXAMPLES:
sage: R.<x> = QQ[] sage: f = x^5 + x + 1 sage: X = HyperellipticCurve(f) sage: J = Jacobian(X) sage: K = KummerSurface(J); K Closed subscheme of Projective Space of dimension 3 over Rational Field defined by: X0^4 - 4*X0*X1^3 + 4*X0^2*X1*X2 - 4*X0*X1^2*X2 + 2*X0^2*X2^2 + X2^4 - 4*X0^3*X3 - 2*X0^2*X1*X3 - 2*X1*X2^2*X3 + X1^2*X3^2 - 4*X0*X2*X3^2
>>> from sage.all import * >>> R = QQ['x']; (x,) = R._first_ngens(1) >>> f = x**Integer(5) + x + Integer(1) >>> X = HyperellipticCurve(f) >>> J = Jacobian(X) >>> K = KummerSurface(J); K Closed subscheme of Projective Space of dimension 3 over Rational Field defined by: X0^4 - 4*X0*X1^3 + 4*X0^2*X1*X2 - 4*X0*X1^2*X2 + 2*X0^2*X2^2 + X2^4 - 4*X0^3*X3 - 2*X0^2*X1*X3 - 2*X1*X2^2*X3 + X1^2*X3^2 - 4*X0*X2*X3^2