# projections -- projections of a multi-projective variety

## Synopsis

• Usage:
projections X
• Inputs:
• X, , a subvariety of $\mathbb{P}^{k_1}\times\mathbb{P}^{k_2}\times\cdots\times\mathbb{P}^{k_n}$
• Outputs:
• the list of the projections $X\to \mathbb{P}^{k_i}$, for $i=1,\ldots,n$

## Description

 i1 : X = projectiveVariety(ZZ/101[x_0..x_3]) ** projectiveVariety(ZZ/101[y_0..y_2]); o1 : ProjectiveVariety, PP^3 x PP^2 i2 : projections X o2 = {-- rational map -- , ZZ ZZ source: Proj(---[x0 , x0 , x0 , x0 ]) x Proj(---[x1 , x1 , x1 ]) 101 0 1 2 3 101 0 1 2 ZZ target: Proj(---[x , x , x , x ]) 101 0 1 2 3 defining forms: { x0 , 0 x0 , 1 x0 , 2 x0 3 } ------------------------------------------------------------------------ -- rational map -- } ZZ ZZ source: Proj(---[x0 , x0 , x0 , x0 ]) x Proj(---[x1 , x1 , x1 ]) 101 0 1 2 3 101 0 1 2 ZZ target: Proj(---[y , y , y ]) 101 0 1 2 defining forms: { x1 , 0 x1 , 1 x1 2 } o2 : List

## Ways to use projections :

• "projections(MultiprojectiveVariety)"

## For the programmer

The object projections is .