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projectionMaps -- projections of a multi-projective variety

Synopsis

Usage:

projectionMaps X
Inputs:
- X, a multi-projective variety, 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 = random({{1,1},{1,1}},0_(PP_(ZZ/101)^{3,1}));

o1 : ProjectiveVariety, surface in PP^3 x PP^1

i2 : p = projectionMaps X;

i3 : p_0

o3 = multi-rational map consisting of one single rational map
     source variety: surface in PP^3 x PP^1 cut out by 3 hypersurfaces of multi-degrees (1,1)^2 (2,0)^1 
     target variety: surface in PP^3 defined by a form of degree 2
     dominance: true

o3 : MultirationalMap (dominant rational map from X to surface in PP^3)

i4 : p_1

o4 = multi-rational map consisting of one single rational map
     source variety: surface in PP^3 x PP^1 cut out by 3 hypersurfaces of multi-degrees (1,1)^2 (2,0)^1 
     target variety: PP^1
     dominance: true

o4 : MultirationalMap (dominant rational map from X to PP^1)

See also

projections -- projections of a multi-projective variety

Ways to use projectionMaps:

projectionMaps(MultiprojectiveVariety)
projectionMaps(MultirationalMap) -- get the compositions of the multi-rational map with the projections of the target

For the programmer

The object projectionMaps is a method function.