gausskImage -- computes the image of the Gauss map of order k

Synopsis

• Usage:

  gausskImage(A,k)

• Inputs:
  • A, a matrix, or a a list where the columns are lattice points
  • k, an integer
• Outputs:
  • a list, of monomials giving the torus embedding via the Plücker embedding of the image of the Gauss map of order k for generically k-jet spanned the toric variety X_A

Description

gausskImage is a function. It computes the image of the Gauss map of order k embedded via the Plücker embedding as described in the paper A note on higher order Gauss maps

i1 : P=hypercube(2,1);

i2 : Q=convexHull(matrix{{0}});

i3 : A=latticePoints(P);

i4 : B=latticePoints(cayley({Q,Q,Q},2));

i5 : gausskImage(A,2)

       -2   -2 -2   -1 -2   -1   -2 -1   -1 -1         -2   -1      -2     -1   -1         -2     2   2 -2   2 -1         2   
o5 = {x  , x  x  , x  x  , x  , x  x  , x  x  , x , x x  , x  , 1, x  , x x  , x  x , x , x  x , x , x x  , x x  , x x , x x ,
       1    0  1    0  1    1    0  1    0  1    0   0 1    0       0    0 1    0  1   1   0  1   0   0 1    0 1    0 1   0 1 
     ----------------------------------------------------------------------------------------------------------------------------
        2   2 2   2   -1 2   -2 2
     x x , x x , x , x  x , x  x }
      0 1   0 1   1   0  1   0  1

o5 : List

i6 : gausskImage(B,2)

       4 4
o6 = {x x }
       0 1

o6 : List

See also

• gaussImage -- computes the image the Gauss map
• gaussFiber -- computes the general fiber of the Gauss map
• gausskFiber -- computes the general fiber of the Gauss map of order k