regularitySequence -- regularity of Ext modules for a sequence of MCM approximations

Synopsis

• Usage:

  L = regularitySequence (R,M)

• Inputs:
  • R, a list, list of rings R_i = S/(f_0..f_{(i-1)}), complete intersections
  • M, a module, module over R_c where c = length R - 1.
• Outputs:
  • L, a list, List of pairs {regularity evenExtModule M_i, regularity oddExtModule M_i)

Description

i1 : c = 3;d=2

o2 = 2

i3 : R = setupRings(c,d);

i4 : Rc = R_c

o4 = Rc

o4 : QuotientRing

i5 : M = coker matrix{{Rc_0,Rc_1,Rc_2},{Rc_1,Rc_2,Rc_0}}

o5 = cokernel | x_0 x_1 x_2 |
              | x_1 x_2 x_0 |

                              2
o5 : Rc-module, quotient of Rc

i6 : regularitySequence(R,M)
reg even ext, soc degs even ext, reg odd ext, soc degs odd ext

{3, {1, 1, 1}, 2, {1, 1}}
{2, {0, 0, 0, 1}, 2, {0, 0, 0}}
{0, {}, 0, {}}

See also

• approximation -- returns pair of components of the map from the MCM approximation
• auslanderInvariant -- measures failure of surjectivity of the essential MCM approximation