Home Online Manual
Top
Back: twist
Forward: regionComplex
FastBack:
FastForward:
Up: tateProdCplxNegGrad_lib
Top: Singular Manual
Contents: Table of Contents
Index: Index
About: About this document

D.15.21.12 beilinsonWindow

Procedure from library tateProdCplxNegGrad.lib (see tateProdCplxNegGrad_lib).

Usage:
beilinsonWindow(T); T multigradedcomplex

Purpsose:
compute the subquotient complex of T consisting of summands generated in degrees 0 <= a <= n

Assume:
T is a multigraded complex of free E-modules

Return:
multigradedcomplex, the Beilinson window of T

Note:
The returend summands are the only ones that contribute to the Beilinson monad.

Example:
 
LIB "tateProdCplxNegGrad.lib";
intvec f = 1,1;
def (S,E) = productOfProjectiveSpaces(f);
intvec low = -3,-3;
intvec high = 3,3;
setring(S);
module M = 0;
intmat MGrading[2][1] = -1,-1;
M = setModuleGrading(M,MGrading);
multigradedcomplex tate;
(E,tate) = tateResolution(M,low,high);
setring(E);
multigradedcomplex W = beilinsonWindow(tate);
W;
==> 0  <--  E^4  <--  E^4  <--  E^1  <--  0
==> -1      0         1         2         3
==> 
intvec c = 1,1,1;
intvec low2 = 0,0,0;
intvec high2 = 0,1,0;
def (S2,E2) = productOfProjectiveSpaces(c);
setring(S2);
module M2 = 0;
intmat gradeM[3][1] = -1,-1,-1;
M2 = setModuleGrading(M2,gradeM);
multigradedcomplex tate2;
(E2,tate2) = tateResolution(M2,low2,high2);
setring(E2);
multigradedcomplex W2 = beilinsonWindow(tate2);
W2;
==> 0  <--  E^8
==> -1      0
==>