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Results tagged with complex-geometry
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user 1887
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.
3
votes
1
answer
882
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Existence of constant scalar curvature Kahler metrics on projective manifolds
It is well known that the blow-up of $\mathbb P^2$ in one or two points does not accept a Kahler-Einstein metric. Kahler-Einstein metrics are particular cases of constant scalar curvature Kahler metri …
- 2,215
2
votes
2
answers
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Applications of Slope Stability
Ross and Thomas developed slope-stability of $(X,L)$ where $X$ is an $L$-polarised variety and $L$ is an ample line bundle, as an obstruction to K-stability of $(X,L)$.
DISCLAIMER: (Forgive me if I d …
- 2,215
6
votes
2
answers
2k
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Generalisations of Riemann-Roch for surfaces
Let $X$ be a smooth projective algebraic surface (over $\mathbb{C}$ ). For all $L\in \mathrm{Pic}(X)$, we have
$$\chi(L)=\chi(\mathcal{O}_X)+\frac{1}{2}(L^2-L\cdot \omega_X).$$
This is the famous Riem …
- 2,215