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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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