Blowing up

In mathematics, blowing up is a type of geometric modification, particularly applied in algebraic geometry, where it is essential in birational geometry. At a point Z that is being 'blown up' (the metaphor is inflation of a balloon, rather than explosion), Z is replaced by the whole space of tangent directions at Z (which, more formally, can be defined as the projective space constructed from the tangent space at Z). More general blow-ups are also defined.

Related Topics:
Mathematics - Algebraic geometry - Birational geometry - Projective space - Tangent space

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