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Results tagged with algebraic-surfaces
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user 5328
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.
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Rational curves on varieties of general type
Let $S$ be a complex surface of general type. Are there infinitely many smooth rational curves on $S$? And more general, what if $V$ is a variety of general type?
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On a result about genus two pencils
I am reading the paper "Canonical models of surfaces of general type" by E. Bombieri. In the last section of this paper, there is a statement saying that surfaces with $K^2=1$ and $p_g=0$ do not have …
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On base locus of canoncal linear system on surfaces
Let $S$ be a minimal surface of general type over $\mathbb{C}$ with $p_g=h^0(K_S)>1$. As a convention, we can write $|K_S|=|M|+F$ such that $F$ is the fixed part. We know that $K_SM \le K_S^2$.
Howe …
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