dualDegCodim -- Computes the degree and codimension of the dual to a projective toric variety

Synopsis

• Usage:

  dualDegCodim(A)

• Inputs:
  • A, a matrix, a full rank integer matrix with the vector (1,1,...,1) in its row space defining a projective toric variety X_A
• Optional inputs:
  • ForceAmat (missing documentation) => a Boolean value, default value false, if A defines a codimension two toric variety a faster method will be used by default, setting this to true forces the general purpose method
• Outputs:
  • degCodim, a hash table, the polar degrees of the projective toric variety X_A.

Description

i1 : A=matrix{{0, 0, 0, 1, 1,5},{7,0, 1, 3, 0, -2},{1,1, 1, 1, 1, 1}}

o1 = | 0 0 0 1 1 5  |
     | 7 0 1 3 0 -2 |
     | 1 1 1 1 1 1  |

              3        6
o1 : Matrix ZZ  <--- ZZ

i2 : dc=dualDegCodim(A)


o2 = HashTable{dualCodim => 1  }
               dualDegree => 53

o2 : HashTable

i3 : dc#"dualCodim"

o3 = 1

i4 : dc#"dualDegree"

o4 = 53

o4 : QQ

i5 : pd=polarDegrees(A);

The toric variety has degree = 35
The dual variety has degree = 53, and codimension = 1
Chern-Mather Volumes: (V_0,..,V_(d-1)) = {-12, 20, 35}
Polar Degrees: {53, 85, 35}
ED Degree = 173

                         5      4      3
Chern-Mather Class: - 12h  + 20h  + 35h