Singularities of Varieties
Singularities of Varieties
Singularities of Varieties
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The Vanishing Ideal<br />
Let R := K[[x 1 , ...,x n ]] be the ring <strong>of</strong> convergent power series. Let<br />
V ⊆ U ⊆ K n be a singularity. Then Ideal(V ) is defined as the ideal <strong>of</strong> all<br />
f ∈ R that vanish at all points in V . It does not depend on the choice <strong>of</strong><br />
the representative.<br />
Any ideal <strong>of</strong> R is finitely generated. Vanishing ideals are radical. The<br />
converse holds for the case K = C, but not for the case K = R.<br />
VO AAG 2