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ToricInvariants :: dualDegCodim

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

Synopsis

Description

This function computes the degree and codimension of the projective toric variety XA, we do not assume that XA is normal. This function uses polarDegrees internally and this information can also be obtained from the polarDegrees function.

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

Ways to use dualDegCodim :