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Results tagged with algebraic-surfaces
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user 16751
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.
10
votes
Generalisations of Riemann-Roch for surfaces
The adjunction formula in the form
$$
\omega_C \cong \omega_X(C)|_C
$$
holds whenever $C$ is a Cartier divisor on a Gorenstein scheme $X$. Taking Euler characteristics, you get an extremely general g …
- 1,279
10
votes
Divisorial contraction: when is the image an algebraic space or a stack?
In order to have a contraction morphism $X\to Y$, the intersection matrix must be negative definite.
Conversely, if the intersection matrix is negative definite, the contraction morphism exists in th …
- 1,279
5
votes
every involution of an Enriques surface is
Yes! However, as Rita, Torsten and Ru pointed out, my first ideas were too simple-minded. Although this makes the remarks by them somewhat unreadable, let me give the corrected answer:
So, let $X$ be …
- 1,279
4
votes
Quotients of rational surfaces
Just to round out the picture: if the characteristic of $k$ is positive and $G$ is a finite, but non-reduced group scheme (for example, the infinitesimal group scheme $\mu_p$ of $p$.the roots of unity …
- 1,279