codim(CoherentSheaf) -- codimension of the support of a coherent sheaf on a projective variety
Synopsis
-
Function: codim
-
- Usage:
codim F
-
Inputs:
-
Optional inputs:
-
Generic (missing documentation)
=> ..., default value false,
-
Outputs:
Description
Computes the codimension of the support of
F as given by
dim(R) - dim(M) where
M is the module representing
F over the homogeneous coordinate ring
R of
X.
i1 : R = ZZ/31991[a,b,c,d];
|
i2 : I = monomialCurveIdeal(R,{1,3,5})
2 2 2 3 2
o2 = ideal (c - b*d, b c - a d, b - a c)
o2 : Ideal of R
|
i3 : projplane = Proj(R)
o3 = projplane
o3 : ProjectiveVariety
|
i4 : II = sheaf module I
o4 = image | c2-bd b2c-a2d b3-a2c |
1
o4 : coherent sheaf on projplane, subsheaf of OO
projplane
|
i5 : can = sheafExt^1(II,OO_projplane^1(-4))
o5 = cokernel | c b a2 |
| d c b2 |
2
o5 : coherent sheaf on projplane, quotient of OO
projplane
|
i6 : codim can
o6 = 2
|
Caveat
The returned value is the usual codimension if R is an integral domain or, more generally, equidimensional.