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.
Where this leads
10 pages build on this one.
Further reading
About this page
| Tag | C4KGYAFPN7 |
|---|---|
| URI | m2://C4KGYAFPN7 |
| Kind | concept |
| Writing | W0 stub |
| MSC | 14E05, 14E15 |
| Same as |
Markdown · JSON · Edit on GitHub
What this page needs for W1
- a source with a locator (0 of 1)
The writing levels say how complete the text of a page is. They do not measure its truth.
What links here
Used by
- Modification of a complex space
- Del Pezzo surface
- Hironaka's resolution for complex spaces
- Resolution of singularities
- Twenty-seven lines on a cubic surface
- Castelnuovo's contraction theorem