i1 : X = abstractProjectiveSpace' 4 o1 = X o1 : a flag bundle with subquotient ranks {4, 1} |
i2 : OO_X(3) o2 = a sheaf o2 : an abstract sheaf of rank 1 on X |
i3 : chi oo o3 = 35 |
i4 : pt = base n o4 = pt o4 : an abstract variety of dimension 0 |
i5 : Y = abstractProjectiveSpace'(4,pt) o5 = Y o5 : a flag bundle with subquotient ranks {4, 1} |
i6 : OO_Y(n) o6 = a sheaf o6 : an abstract sheaf of rank 1 on Y |
i7 : chi oo 1 4 5 3 35 2 25 o7 = --n + --n + --n + --n + 1 24 12 24 12 o7 : QQ[n] |
The notation OO(n) is an abbreviation for OO_X(n), where X is the variety whose intersection ring n is in. By default, the first Chern class of the tautological line bundle on a projective space or projective bundle is called h, so we may use OO(h) as alternative notation for OO_Y(1):
i8 : A = intersectionRing Y o8 = A o8 : QuotientRing |
i9 : chern OO_Y(1) o9 = 1 + h o9 : A |
i10 : OO(h) o10 = a sheaf o10 : an abstract sheaf of rank 1 on Y |
i11 : chern oo o11 = 1 + h o11 : A |
Beware the low parsing precedence of the adjacency operator SPACE.