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

## Synopsis

• 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:
• , 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 $K$

## Description

 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)