EmbeddedProjectiveVariety ++ EmbeddedProjectiveVariety -- join of projective varieties

Synopsis

Operator: ++
Usage:

X ++ Y
Inputs:
- X, an embedded projective variety
- Y, an embedded projective variety, in the same ambient projective space of $X$
Outputs:
- an embedded projective variety, the join of $X$ and $Y$, that is, the closure of the union of lines of the form $\langle p,q\rangle$, with $p\in X$, $q\in Y$, and $p\neq q$

i1 : K = ZZ/333331;

i2 : C = PP_K^(1,5); -- rational normal quintic curve

o2 : ProjectiveVariety, curve in PP^5

i3 : L = linearSpan {point ambient C,point ambient C}; -- random line

o3 : ProjectiveVariety, curve in PP^5

i4 : C ++ L

o4 = threefold in PP^5 cut out by 5 hypersurfaces of degrees 3^4 4^1 

o4 : ProjectiveVariety, threefold in PP^5

i5 : C ++ C

o5 = threefold in PP^5 cut out by 4 hypersurfaces of degree 3

o5 : ProjectiveVariety, threefold in PP^5

i6 : (point C) ++ (point C) ++ (point C)

o6 = surface in PP^5 cut out by 3 hypersurfaces of degree 1

o6 : ProjectiveVariety, surface in PP^5