Singularities of Varieties
Singularities of Varieties
Singularities of Varieties
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Point Blowups in Higher Dimension<br />
The blowup <strong>of</strong> a point in C n is an algebraic map p : Y → C n , where Y is a<br />
manifold that can be covered by n open subsets isomorphic to C n . It has<br />
the following properties:<br />
p −1 (o) is a hypersurface E ⊂ Y. Apart from that, p restricts to an<br />
isomorphism Y − E → C n − {o}. The points <strong>of</strong> E correspond to tangent<br />
directions at o.<br />
VO AAG 37
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