Complex algebraic variety
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In algebraic geometry, a complex algebraic variety is an algebraic variety (in the scheme sense or otherwise) over the field of complex numbers.[1]
Chow's theorem
Chow's theorem states that a projective complex analytic variety, i.e., a closed analytic subvariety of the complex projective space , is an algebraic variety. These are usually simply referred to as
projective varieties
.
Hironaka's theorem
Let X be a complex algebraic variety. Then there is a
projective resolution of singularities
.[2]
Relation with similar concepts
Despite Chow's theorem, not every complex analytic variety is a complex algebraic variety.
See also
References
- ISBN 3-540-54681-2
- ^ (Abramovich 2017)