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MultiprojectiveVarieties :: tangentCone(EmbeddedProjectiveVariety,EmbeddedProjectiveVariety)

tangentCone(EmbeddedProjectiveVariety,EmbeddedProjectiveVariety) -- tangent cone to a projective variety at a point

Synopsis

Description

i1 : Y = random(3,0_(PP_(ZZ/333331)^6)), q = point Y, j = parametrize tangentSpace(Y,q);
i2 : (X, p) = (j^* Y, j^* q);
i3 : C = tangentCone(X,p);

o3 : ProjectiveVariety, hypersurface in PP^5
i4 : describe C

o4 = ambient:.............. PP^5
     dim:.................. 4
     codim:................ 1
     degree:............... 2
     generators:........... 2^1 
     purity:............... true
     dim sing. l.:......... 0
     gens sing. l.:........ 1^5 
i5 : assert(isSubset(C,tangentSpace(X,p)) and coneOfLines(C,p) == C)

See also