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Parameter spaces for conic bundles

A conic bundle over $\mathbb{P}^n$ is a morphism $\pi:X\rightarrow\mathbb{P}^n$ with fibers isomorphic to plane conics. A conic bundle $\pi:X\rightarrow\mathbb{P}^n$ is minimal if it has relative ...
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How to show a contraction of singular moduli space is projective?

Let $\mathcal{H}$ be a certain kind of Hilbert scheme of curves on some smooth projective variety $X$ and $\mathcal{H}$ is projective and irreducible of dimension $3$. There is a divisor $\mathcal{D}\...
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Quasi-projectivity of the moduli space of Kahler-Einstein Fano varities and vanishing Lelong number

Chi Li, Xiaowei Wang, Chenyang Xu proved the Quasi-projectivity of the moduli space of smooth Kahler-Einstein Fano manifolds. My question is about when central fibre $X_0$ along Kahler-Einstein Fano ...
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