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Results tagged with algebraic-surfaces
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user 57030
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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On surfaces of general type wich saturate the BMY-inequality
Let $\mathbb{K}$ an algebraically closed field of characteristic $0$, let $X$ be a smooth minimal surface of general type.
It is known that surfaces satisfy, among other thing, the (Bogomolov-Miayoka- …
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On the positivity of cotangent bundle of elliptic surfaces
I am working on the complex numbers field $\mathbb{C}$, for simplicity. However you can relax this assumption if you want.
Let $X$ be an elliptic surface, id est there is a proper morphism $\pi\colon …
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Existence of elliptic curves on surfaces of general type
Let $X$ be a complex minimal surface of general type, id est $K_X$ is big and nef. It is well-known that $\displaystyle\int_X3c_2(X)-c_1(X)^2\geq0$, and the equality holds if and only if $X$ is unifor …
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On the birational equivalent class of algebraic surfaces with Picard number $1$
An open subset $U$ of a projective surface $Z$ is big if $\mathrm{codim}_Z(Z\setminus U)\geq2$.
Let $X$ and $Y$ be smooth complex projective surface. If there exists a birational map $f:X\dashrightarr …
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On the positivity of the second Segre class of ample vector bundles
Let $E$ be an ample rank $r\geq2$ vector bundle over a smooth projective surface $X$ defined on an algebraically closed field $\mathbb{K}$ of characteristic $0$.
In Kleiman S. L. - Ample Vector Bundle …
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BMY inequality for surfaces of general type in characteristic 0
Let $X$ be a smooth, complex, projective, minimal surface of general type, i.e. the canonical (line) bundle $K_X$ is big and nef.
It is known that $3c_2\geq c_1^2$ (the Bogomolov-Miyaoka-Yau inequalit …
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