Singularities of Varieties
Singularities of Varieties
Singularities of Varieties
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Other Cases<br />
m = 1, n = 2: locally stable iff nonsingular, stable iff image has only<br />
ordinary double points.<br />
m = 1,n > 2: stable iff immersion as a submanifold<br />
n = 1: Morse theorem.<br />
m = 2, n = 3: locally stable iff nonsingular or (x, y) ↦→ (xy, y, x 2 ). Stable<br />
iff image has local equation x = 0 or xy = 0 or xyz = 0 or x 2 − y 2 z = 0.<br />
m = n ≥ 9: stable maps are not dense!<br />
VO AAG 33
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