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Let $\mathcal M^{(X,D)}$ be a moduli space of pair varieties $(X,D)$ which $K_X+D$ is trivial and $D$ is a divisor with conic singularities on Kaehler variety $X$. I am looking for a proof that such ...

Let $\mathcal M_g$ be the moduli space of curves of genus $g$. If we take $X^{reg}=X\setminus D$, where D is a divisor with normal crossings. Endow $X^{reg}$ with a complete Kahler metric which has a ...