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Divisor :: nonCartierLocus

nonCartierLocus -- the non-Cartier locus of a Weil divisor

Synopsis

Description

Returns an ideal which vanishes on the locus where D is not Cartier.

i1 : R = QQ[x, y, u, v]/ideal(x * y  - u * v);
i2 : D = divisor({1, -3, -5, 8}, {ideal(x, u), ideal(y, v), ideal(x, v), ideal(y, u)})

o2 = -5*Div(x, v) + 8*Div(y, u) + Div(x, u) + -3*Div(y, v)

o2 : WeilDivisor on R
i3 : nonCartierLocus( D )

             5     4     4     4   2 3       3       3   2 3   2 3   3 2 
o3 = ideal (v , u*v , y*v , x*v , u v , y*u*v , x*u*v , y v , x v , u v ,
     ------------------------------------------------------------------------
        2 2     2 2   2   2   2   2   3 2   3 2   4      3      3    2 2  
     y*u v , x*u v , y u*v , x u*v , y v , x v , u v, y*u v, x*u v, y u v,
     ------------------------------------------------------------------------
      2 2    3      3      4    4    5     4     4   2 3   2 3   3 2   3 2 
     x u v, y u*v, x u*v, y v, x v, u , y*u , x*u , y u , x u , y u , x u ,
     ------------------------------------------------------------------------
      4    4    5   5
     y u, x u, y , x )

o3 : Ideal of R

If the option IsGraded is set to true (by default it is false), it saturates with respect to the homogeneous maximal ideal.

i4 : R = QQ[x, y, u, v]/ideal(x * y  - u * v);
i5 : D = divisor({1, -3, -5, 8}, {ideal(x, u), ideal(y, v), ideal(x, v), ideal(y, u)})

o5 = -5*Div(x, v) + 8*Div(y, u) + Div(x, u) + -3*Div(y, v)

o5 : WeilDivisor on R
i6 : nonCartierLocus( D, IsGraded => true )

o6 = ideal 1

o6 : Ideal of R

See also

Ways to use nonCartierLocus :