# codim(CoherentSheaf) -- codimension of the support of a coherent sheaf on a projective variety

## 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)) -- ker (109) called with OptionTable: OptionTable{SubringLimit => infinity} -- ker (109) returned CacheFunction: -*a cache function*- -- ker (109) called with Matrix: 0 -- 2 -- ker (109) returned Module: R assert( ker(map(R^0,R^2,0)) === (R^2)) -- ker (110) called with OptionTable: OptionTable{SubringLimit => infinity} -- ker (110) returned CacheFunction: -*a cache function*- -- ker (110) called with Matrix: 0 -- 3 -- ker (110) returned Module: R assert( ker(map(R^0,R^{{-2}, {-1}, {-1}},0)) === (R^{{-2}, {-1}, {-1}})) 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.