Returns true if the divisor is simple normal crossings, this includes checking that the ambient ring is regular.
i1 : R = QQ[x, y, z] / ideal(x * y - z^2 ); |
i2 : D = divisor({1, -2}, {ideal(x, z), ideal(y, z)}) o2 = -2*Div(y, z) + Div(x, z) o2 : WeilDivisor on R |
i3 : isSNC( D ) o3 = false |
i4 : R = QQ[x, y]; |
i5 : D = divisor(x*y*(x+y)) o5 = Div(x+y) + Div(x) + Div(y) o5 : WeilDivisor on R |
i6 : isSNC( D ) o6 = false |
i7 : R = QQ[x, y]; |
i8 : D = divisor(x*y*(x+1)) o8 = Div(x+1) + Div(x) + Div(y) o8 : WeilDivisor on R |
i9 : isSNC( D ) o9 = true |
If IsGraded is set to true (default false), then the divisor is treated as if it is on the Proj of the ambient ring. In particular, non-SNC behavior at the origin in ignored.
i10 : R = QQ[x, y, z] / ideal(x * y - z^2 ); |
i11 : D = divisor({1, -2}, {ideal(x, z), ideal(y, z)}) o11 = -2*Div(y, z) + Div(x, z) o11 : WeilDivisor on R |
i12 : isSNC( D, IsGraded => true ) o12 = true |
i13 : R = QQ[x, y]; |
i14 : D = divisor(x*y*(x+y)) o14 = Div(x) + Div(y) + Div(x+y) o14 : WeilDivisor on R |
i15 : isSNC( D, IsGraded => true ) o15 = true |
i16 : R = QQ[x,y,z]; |
i17 : D = divisor(x*y*(x+y)) o17 = Div(y) + Div(x) + Div(x+y) o17 : WeilDivisor on R |
i18 : isSNC( D, IsGraded => true) o18 = false |