Description
Given a weakly decreasing list of integers L of length n and an integer u, uses Bott's algorithm to compute the cohomology of the vector bundle E=O(-u) \tensor S_L(Q), on P^n = PP(V) where Q is the tautological rank n quotient bundle in the sequence 0--> O(-1) --> O^(n+1) --> Q -->0 and S_L(Q) is the Schur functor with the convention S_(d,0..0) = Sym_d, S_(1,1,1) = \wedge^3 etc. Returns either 0, if all cohomology is zero, or a list of three elements: A weakly decreasing list of n+1 integers M; a number i such that H^i(E)=S_M(V); and the rank of this module. For more information on how the partition M is constructed, see math.AC/0709.1529v3, "The Existence of Pure Free Resolutions", section 3.
For example, on P^3, E = S_3(Q) has H^0(S_3(Q)) = S_3(kk^4) = kk^20.
i1 : bott({3,0,0},0)
o1 = {{3, 0, 0, 0}, 0, 20}
o1 : List
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H^*(E(-1)) = H^*(E(-2)) = 0, and H^2(E(-3)) == S_2(kk^4) == kk^10.
i2 : bott({3,0,0},1)
o2 = 0
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i3 : bott({3,0,0},2)
o3 = 0
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i4 : bott({3,0,0},3)
o4 = {{2, 0, 0, 0}, 2, 10}
o4 : List
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i5 : bott({2,1,0},0)
o5 = {{2, 1, 0, 0}, 0, 20}
o5 : List
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