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Results tagged with algebraic-surfaces
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user 8003
An algebraic surface is an algebraic variety of dimension two. In the case of geometry over the field of complex numbers, an algebraic surface has complex dimension two (as a complex manifold, when it is non-singular) and so of dimension four as a smooth manifold.
8
votes
1
answer
2k
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Contracting a curve of negative self-intersection on a surface
It is easy to show using birational factorization that the only curves on a surface which can be contracted to get an algebraic, smooth surface are smooth $(-1)$-curves. Furthermore, I know of example …
- 1,493
5
votes
1
answer
337
views
Quotient of a smooth projective surface by an involution
Is the quotient of a smooth complex projective surface by an involution projective? Suppose the quotient happens to be smooth; does that change the situation?
- 1,493