projectiveVariety(List,List,Ring) -- the Segre-Veronese variety

• Function: projectiveVariety

• Usage:

  projectiveVariety(n,d,K)

  PP_K^(n,d)

• Inputs:
  • n, a list, a list of $r$ non-negative integers $n=\{n_1,n_2,\ldots,n_r\}$
  • d, a list, a list of $r$ degrees $d=\{d_1,d_2,\ldots,d_r\}$
  • K, a ring, a field
• Optional inputs:
  • MinimalGenerators => ..., default value true, whether to trim the ideal (intended for internal use only)
  • Saturate => ..., default value true, whether to compute the multi-saturation of the ideal (intended for internal use only)
• Outputs:
  • a multi-projective variety, the Segre-Veronese variety $\nu_{d_1}(\mathbb{P}^{n_1})\times\nu_{d_2}(\mathbb{P}^{n_2})\times\cdots\times\nu_{d_r}(\mathbb{P}^{n_r})$ over $K$

i1 : X = projectiveVariety({2,1,3},{3,4,2},ZZ/33331);

o1 : ProjectiveVariety, 6-dimensional subvariety of PP^9 x PP^4 x PP^9

i2 : X = PP_(ZZ/33331)^({2,1,3},{3,4,2});

o2 : ProjectiveVariety, 6-dimensional subvariety of PP^9 x PP^4 x PP^9

i3 : parametrize X;

o3 : MultirationalMap (rational map from PP^6 to X)