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Divisor :: mapToProjectiveSpace

mapToProjectiveSpace -- Calculate the double dual of an ideal

Synopsis

Description

Given a Cartier divisor D on a projective variety (represented by a divisor on a normal 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)

o1 = R

o1 : QuotientRing
i2 : D = divisor( ideal(x, u) )

o2 = 1*Div(u, x) of R

o2 : WDiv
i3 : mapToProjectiveSpace(D)

o3 = map(R,QQ[YY , YY ],{u, y})
                1    2

o3 : RingMap R <--- QQ[YY , YY ]
                         1    2
i4 : R = ZZ/7[x,y,z]

o4 = R

o4 : PolynomialRing
i5 : D = divisor(x*y)

o5 = 1*Div(y) + 1*Div(x) of R

o5 : WDiv
i6 : mapToProjectiveSpace(D)

           ZZ                                 2             2        2
o6 = map(R,--[YY , YY , YY , YY , YY , YY ],{x , x*y, x*z, y , y*z, z })
            7   1    2    3    4    5    6

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

See also

Ways to use mapToProjectiveSpace :