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ample (Definition)

An invertible sheaf $ \L$ on a scheme $ X$ is called ample if for any coherent sheaf $ \mathfrak{F}$, $ \mathfrak{F}\otimes\L ^n$ is generated by global sections for sufficiently large $ n$.

An invertible sheaf is ample if and only if $ \L ^m$ is very ample for some $ m$; this is very often taken as the definition of ample, which can be surprising.



"ample" is owned by archibal. [ full author list (3) | owner history (2) ]
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Cross-references: very ample, global sections, generated by, coherent sheaf, scheme, invertible sheaf
There are 3 references to this entry.

This is version 3 of ample, born on 2003-08-19, modified 2004-03-29.
Object id is 4622, canonical name is Ample.
Accessed 2449 times total.

Classification:
AMS MSC: 14A99 (Algebraic geometry :: Foundations :: Miscellaneous)
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