projectiveBundle -- make a projective bundle from an abstract sheaf

Synopsis

• Usage:

  projectiveBundle F

  projectiveBundle(n,X)

  projectiveBundle n

• Inputs:
  • F, an abstract sheaf,
  • n, an integer,
  • X, an abstract variety,
• Optional inputs:
  • VariableNames => a thing, default value null, see flagBundle(...,VariableNames=>...)
• Outputs:
  • the projective bundle of rank 1 sub-bundles of the abstract sheaf $F$. If $F$ is omitted, then a projective space of dimension $n$ over $X$ is produced. If $X$ is omitted, then point is used as the base.

Description

i1 : X = projectiveBundle 4

o1 = X

o1 : a flag bundle with subquotient ranks {1, 4}

i2 : F = OO_X(2) ++ OO_X(3) ++ OO_X(4)

o2 = F

o2 : an abstract sheaf of rank 3 on X

i3 : Y = projectiveBundle F

o3 = Y

o3 : a flag bundle with subquotient ranks {1..2}

i4 : dim Y

o4 = 6

i5 : integral (chern_1 OO_Y(1))^(dim Y)

o5 = 19981

i6 : bundles X/rank

o6 = (1, 4)

o6 : Sequence

Caveat

See also

• projectiveBundle' -- make a projective bundle from an abstract sheaf
• abstractProjectiveSpace -- make a projective space
• flagBundle -- make a flag bundle