D.5.18.6 sheafCohBGGregul_w

Usage:

sheafCohBGGregul_w(M,l,h,w); M module, l,h int, reg int, w intvec

Assume:

M is graded, and it comes assigned with an admissible degree vector w, h>=l, and the basering 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.

Note:

This procedure is based on the Bernstein-Gel'fand-Gel'fand correspondence and on Tate resolution ( see [Eisenbud, Floystad, Schreyer: Sheaf cohomology and free resolutions over exterior algebras, Trans AMS 355 (2003)] ).
sheafCohBGG(M,l,h) does not compute all values in the above table. To determine all values of h^i(F(d)), d=l..h, use sheafCohBGG(M,l-n,h+n).

LIB "sheafcoh.lib";
// cohomology of cotangential bundle on P^3:
//-------------------------------------------
ring R=0,(x,y,z,u),dp;
resolution T1=mres(maxideal(1),0);
module M=T1[3];
intvec v=2,2,2,2,2,2;
def B=sheafCohBGGregul_w(M,-8,4,CM_regularity(M),v);
B;
==> 189,120,70,36,15,4,0,0,0,0,-1,-1,-1,
==> -1,0,0,0,0,0,0,0,0,0,0,-1,-1,
==> -1,-1,0,0,0,0,0,0,1,0,0,0,-1,
==> -1,-1,-1,0,0,0,0,0,0,0,6,20,45