Ideal Quotient - Geometric Interpretation

Geometric Interpretation

The ideal quotient corresponds to set difference in algebraic geometry. More precisely,

  • If W is an affine variety and V is a subset of the affine space (not necessarily a variety), then
I(V) : I(W) = I(V W),

where I denotes the taking of the ideal associated to a subset.

  • If I and J are ideals in k, then
Z(I : J) = cl(Z(I) Z(J))

where "cl" denotes the Zariski closure, and Z denotes the taking of the variety defined by the ideal I.

Read more about this topic:  Ideal Quotient

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