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Results tagged with compactifications
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user 10076
8
votes
Accepted
Non-uniqueness of smooth compactification
The main idea is this: You can always find an $X$ such that $X\supseteq U$ and $X\setminus U\supseteq \Sigma := \mathrm{Sing} X$. Then in characteristic zero apply Hironaka's resolution theorem, which …
- 42.9k
9
votes
Accepted
Uniqueness of smooth compactification upto a smooth morphism
A smooth morphism is flat, and you can't even have a flat morphism between two smooth compactifications.
A flat morphism has equidimensional fibers. …
- 42.9k