i1 : X = projectiveSpace' 4
o1 = X
o1 : a flag bundle with ranks {4, 1}
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i2 : OO_X(3)
o2 = a sheaf
o2 : an abstract sheaf of rank 1 on X
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i3 : chi oo
o3 = 35
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i4 : pt = base n
o4 = pt
o4 : an abstract variety of dimension 0
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i5 : Y = projectiveSpace'(4,pt)
o5 = Y
o5 : a flag bundle with ranks {4, 1}
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i6 : OO_Y(n)
o6 = a sheaf
o6 : an abstract sheaf of rank 1 on Y
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i7 : chi oo
1 4 5 3 35 2 25
o7 = --n + --n + --n + --n + 1
24 12 24 12
o7 : QQ[n]
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The notation OO(n) is an abbreviation for OOX(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 OOY(1):
i8 : A = intersectionRing Y
o8 = A
o8 : QuotientRing
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i9 : chern OO_Y(1)
o9 = 1 + h
o9 : A
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i10 : OO(h)
o10 = a sheaf
o10 : an abstract sheaf of rank 1 on Y
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i11 : chern oo
o11 = 1 + h
o11 : A
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