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D.5.7.6 sheafCoh

Procedure from library sheafcoh.lib (see sheafcoh_lib).

Usage:
sheafCoh(M,l,h); M module, l,h int

Assume:
M is graded, and it comes assigned with an admissible degree vector as an attribute, h>=l. The basering S has n+1 variables.

Return:
intmat, cohomology of twists of the coherent sheaf F on P^n associated to coker(M). The range of twists is determined by l, h.

Display:
The intmat is displayed in a diagram of the following form:
 
                l            l+1                      h
  ----------------------------------------------------------
      n:     h^n(F(l))    h^n(F(l+1))   ......    h^n(F(h))
           ...............................................
      1:     h^1(F(l))    h^1(F(l+1))   ......    h^1(F(h))
      0:     h^0(F(l))    h^0(F(l+1))   ......    h^0(F(h))
  ----------------------------------------------------------
    chi:     chi(F(l))    chi(F(l+1))   ......    chi(F(h))
A '-' in the diagram refers to a zero entry.

Note:
The procedure is based on local duality as described in [Eisenbud: Computing cohomology. In Vasconcelos: Computational methods in commutative algebra and algebraic geometry. Springer (1998)].
By default, the procedure uses mres to compute the Ext modules. If called with the additional parameter "sres", the sres command is used instead.

Example:
 
See also: dimH; sheafCohBGG.


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