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We say that a projective variety $X$ is of general type if the Kodaira dimension is equal to the dimension of $X$., i.e. $\text{kod}(X)=\dim X$. When $K_X$ is positive then by the result of S.T.Yau w …

Let $\mathcal X\to \mathcal S$, be a family of polarized Kaehler manifolds with $\omega_s= Ric(\omega_s)$(i.e., fibers are Fano Kahler-Einstein manifolds). Then $dim Aut(X_s)=Const$.? Is there any co …

Let $π:X→Δ$ be a family of compact complex manifolds such that the fibre $X_t:=π^{−1}(t)$ admits a Kaehler-Einstein metric of negative Ricci curvature for all $t≠0$. Then does the special fiber $X_0:= …

Consider a Kaehler degeneration $\mathcal X\to \Delta$ of smooth manifolds: Here $\Delta$ is the unit disc, $\pi$ a proper flat map, smooth over $\Delta^∗=\Delta−\{0\}$. The general fibres are $X_t=\ …

Let $\pi:\mathcal X\to B$ be a family of Kaehler manifolds then if we take $B'\subset B$ be the set of parameters such that $X_b$ admit Kaehler-Einstein metric(with zero, negative, or positive Ricci c …