next | previous | forward | backward | up | top | index | toc | Macaulay2 website
ResidualIntersections :: linkageBound

linkageBound -- computes a bound on the number of general links of an ideal to test the licci property



An ideal I in a polynomial ring S is licci if it Cohen-Macaulay and is linked in finitely many steps I --> (F):I, where F is a maximal regular sequence in I, to a complete intersection. Bernd Ulrich showed that if I is licci and each step of the linkage is done via a regular sequence F that is a subset of a minimal set of generators, then the linkage process will terminate after at most b steps, where

b = 2(codim I)*(degree I -1) -6.

(Theorem 2.4 of "On Licci Ideals", Contemp. Math 88 (1989). This is computed by linkageBound I. He did this via a more refined formula; the (generally sharper) intermediate result gives the bound

b = 2(numgens(Hom(I, S/I) - codim I).

The call linkageBound(I, UseNormalModule =>true) computes this refined bound. See isLicci for examples.


The crude bound can be quite large; computing the refined bound (which is often large as well) can be quite slow.

See also

Ways to use linkageBound :

For the programmer

The object linkageBound is a method function with options.