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MultiprojectiveVarieties :: linearlyNormalEmbedding

linearlyNormalEmbedding -- get the linearly normal embedding

Synopsis

Description

i1 : K = ZZ/333331;
i2 : X = PP_K^(1,7); -- rational normal curve of degree 7

o2 : ProjectiveVariety, curve in PP^7
i3 : time f = linearlyNormalEmbedding X;
     -- used 0.00946185 seconds

o3 : MultirationalMap (automorphism of X)
i4 : Y = (rationalMap {for i to 3 list random(1,ring ambient X)}) X; -- an isomorphic projection of X in PP^3

o4 : ProjectiveVariety, curve in PP^3
i5 : time g = linearlyNormalEmbedding Y;
     -- used 0.536626 seconds

o5 : MultirationalMap (birational map from Y to curve in PP^7)
i6 : assert(isIsomorphism g)
i7 : describe g

o7 = multi-rational map consisting of one single rational map
     source variety: curve in PP^3 cut out by 6 hypersurfaces of degree 4
     target variety: curve in PP^7 cut out by 21 hypersurfaces of degree 2
     base locus: empty subscheme of PP^3
     dominance: true
     multidegree: {7, 7}
     degree: 1
     degree sequence (map 1/1): [3, 3, 3, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4]
     coefficient ring: K

Caveat

This is an experimental function.

Ways to use linearlyNormalEmbedding :

For the programmer

The object linearlyNormalEmbedding is a method function.