poincareDuality -- Apply the isomorphism Hom(A^k(X),ZZ) = A_k(X)

Synopsis

• Usage:

  poincareDuality(l, X, k)

• Inputs:
  • l, a list,
  • X, a normal toric variety,
  • k, an integer,
• Outputs:
  • Y, a list,

Description

i1 : X = toricProjectiveSpace 3;

i2 : k = 2;

i3 : l = toList(#orbits(X,1):3)

o3 = {3, 3, 3, 3, 3, 3}

o3 : List

i4 : poincareDuality(l, X, k)

o4 = {3, 0, 0, 0}

o4 : List

i5 : poincareMatrix(X,2)

o5 = | 1 1 1 1 |
     | 1 1 1 1 |
     | 1 1 1 1 |
     | 1 1 1 1 |
     | 1 1 1 1 |
     | 1 1 1 1 |

              6        4
o5 : Matrix QQ  <--- QQ