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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 , Z , Z , Z , Z ],{x , x*y, x*z, y , y*z, z })
            7  1   2   3   4   5   6

                    ZZ
o6 : RingMap R <--- --[Z , Z , Z , Z , Z , Z ]
                     7  1   2   3   4   5   6

See also

Ways to use mapToProjectiveSpace :