Morphism from projective space to product of projective spaces

AlgebraicGeometry

asked 2020-06-10 15:48:09 +0100

JNS
25 ●4

I have a problem with creating a rational map from the projective plane to P^1xP^1. The following code gives the error "polys (=[x, y, x^2, y^2]) must be of the same degree":

K = GF(2)
P2.<x,y,z> = ProjectiveSpace(K,2)
P1P1.<x0,x1,y0,y1> = ProductProjectiveSpaces([1,1],K)
H = Hom(P2,P1P1)
H([x,y,x^2,y^2])

On the other hand, creating the "same" map on P^1xP^1 does not give an error:

E = End(P1P1)
E([x0,x1,x0^2,x1^2])

Can someone explain to me why it does not work and how I can go around this problem?

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answered 2020-06-11 10:31:16 +0100

mwageringel
691 ●10 ●23

Try to upgrade your version of Sage. This works fine in Sage 9.1:

sage: K = GF(2)
....: P2.<x,y,z> = ProjectiveSpace(K,2)
....: P1P1.<x0,x1,y0,y1> = ProductProjectiveSpaces([1,1],K)
....: H = Hom(P2,P1P1)
....: H([x,y,x^2,y^2])
....:
Scheme morphism:
  From: Projective Space of dimension 2 over Finite Field of size 2
  To:   Product of projective spaces P^1 x P^1 over Finite Field of size 2
  Defn: Defined on coordinates by sending (x : y : z) to
        (x : y , x^2 : y^2)

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Asked: 2020-06-10 15:48:09 +0100

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Last updated: Jun 11 '20

Morphism from projective space to product of projective spaces edit

1 Answer