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Divisor :: mapToProjectiveSpace

mapToProjectiveSpace -- compute the map to projective space associated with the global sections of a Cartier divisor

Synopsis

Description

Given a Cartier divisor $D$ on a projective variety (represented by a divisor on a normal standard graded ring), this function returns the map to projective space induced by the global sections of $O(D)$. If KnownCartier is set to false (default is true), the function will also check to make sure the divisor is Cartier away from the irrelevant ideal.

i1 : R = QQ[x,y,u,v]/ideal(x*y-u*v);
i2 : D = divisor( ideal(x, u) )

o2 = Div(x, u)

o2 : WeilDivisor on R
i3 : mapToProjectiveSpace(D)

o3 = map (R, QQ[YY ..YY ], {v, x})
                  1    2

o3 : RingMap R <--- QQ[YY ..YY ]
                         1    2

The user may also specify the variable name of the new projective space.

i4 : R = ZZ/7[x,y,z];
i5 : D = divisor(x*y)

o5 = Div(y) + Div(x)

o5 : WeilDivisor on R
i6 : mapToProjectiveSpace(D, Variable=>"Z")

             ZZ            2             2        2
o6 = map (R, --[Z ..Z ], {x , x*y, x*z, y , y*z, z })
              7  1   6

                    ZZ
o6 : RingMap R <--- --[Z ..Z ]
                     7  1   6

See also

Ways to use mapToProjectiveSpace :

For the programmer

The object mapToProjectiveSpace is a method function with options.