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MultiprojectiveVarieties :: shortcuts

shortcuts -- Some convenient shortcuts for multi-rational maps consisting of a single rational map

Synopsis

i1 : X = PP_QQ^(1,3);

o1 : ProjectiveVariety, curve in PP^3
i2 : a = 4, b = 2;
i3 : phi = rationalMap X;

o3 : MultirationalMap (rational map from PP^3 to PP^2)
i4 : assert(phi <==> multirationalMap {rationalMap ideal X})
i5 : phi = rationalMap(X,a);

o5 : MultirationalMap (rational map from PP^3 to PP^21)
i6 : assert(phi <==> multirationalMap {rationalMap(ideal X,a)})
i7 : phi = rationalMap(X,a,b);

o7 : MultirationalMap (rational map from PP^3 to PP^5)
i8 : assert(phi <==> multirationalMap {rationalMap(ideal X,a,b)})

If you want to consider $X$ as a subvariety of another multi-projective variety $Y$, you may use the command X_Y. For instance, rationalMap(X_Y,a) returns the rational map from $Y$ defined by a basis of the linear system $|H^0(Y,\mathcal{I}_{X\subseteq Y}(a))|$ (basically, this is equivalent to trim((rationalMap(X,a))|Y)).

i9 : Y = random(3,X);

o9 : ProjectiveVariety, surface in PP^3
i10 : rationalMap(X_Y,a);

o10 : MultirationalMap (rational map from Y to PP^17)
i11 : rationalMap X_Y;

o11 : MultirationalMap (rational map from Y to PP^2)

See also