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Complex geometry is the study of complex manifolds, complex algebraic varieties, complex analytic spaces, and, by extension, of almost complex structures. It is a part of differential geometry, algebraic geometry and analytic geometry.
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Stability and Blow up
Let $L$ be a very ample line bundle on a variety $X$ of dimension $n$. The slope of a torsion free sheaf $E$ on $X$ is given by $$\mu_{L}(E) : = \dfrac{c_{1}(E).L^{n-1}}{rank(E)}$$
Let $\pi : \widetil …