T = tateResolution(M,low,high)
phi = tateResolution(A,low,high)
The call
tateResolution(M,low,high)
forms a free subquotient complex the Tate resolution of the sheaf F represented by M in a range that covers all generators corresponding to cohomology groups of twists F(a) of F in the range low <= a <= high, see Tate Resolutions on Products of Projective Spaces.
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The complex contains some trailing terms and superfluous terms in a wider range, which can be removed using trivial homological truncation.
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The call
tateResolution(A,low,high)
where A is a matrix representing the multi-graded module homomorphism from M to N computes the induced map between two free subquotients of Tate resolutions of M and N in the given range.
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The object tateResolution is a method function.
The source of this document is in /build/reproducible-path/macaulay2-1.25.05+ds/M2/Macaulay2/packages/TateOnProducts.m2:5202:0.