normalSheaf -- normal sheaf

Synopsis

• Usage:

  normalSheaf X

  normalSheaf(X % Y)

  normalSheaf(X,Y)

• Inputs:
  • X, an embedded projective variety
  • Y, an embedded projective variety, such that $X\subset Y$ (if not given, it is taken to be the ambient variety of $X$)
• Outputs:
  • a coherent sheaf, the normal sheaf $\mathcal{N}_{X, Y}$ of $X$ in $Y$

Description

i1 : X = PP_(ZZ/65521)^(2,2);

o1 : ProjectiveVariety, surface in PP^5

i2 : Y = random(2,X);

o2 : ProjectiveVariety, hypersurface in PP^5

i3 : N = normalSheaf X;

o3 : Coherent sheaf on X

i4 : N' = normalSheaf(X,Y);

o4 : Coherent sheaf on X

i5 : rank HH^0 N

o5 = 27

i6 : rank HH^0 N'

o6 = 12