Algebraic geometry Birational geometry Concept
Blowing up
Summary
Blowing up is a construction that replaces a closed subvariety of a variety by the set of normal directions to it. The result maps birationally onto the original variety and is an isomorphism away from the centre. The preimage of the centre, the exceptional divisor, is a hypersurface. Blowing up is the basic tool of birational geometry and of resolution of singularities.
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About this page
| Tag | C4KGYAFPN7 |
|---|---|
| URI | m2://C4KGYAFPN7 |
| Kind | concept |
| Writing | W0 stub |
| MSC | 14E05, 14E15 |
| Same as | |
| Changed | 2 November 2026 |
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Used by
- Del Pezzo surface
- Resolution of singularities
- Twenty-seven lines on a cubic surface
- Castelnuovo's contraction theorem