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Motivation: Work of Eisenbud, Harris, and Mumford shows that $\mathcal M_g$ is of general type when $g≥24$. Moreover, by Logan's function $f(g)$ , $\overline {\mathcal M_{g,n}}$ is of general type for ...

Let $X$ be a rational threefold (over the field of complex numbers) with terminal singularities. It is well-known that $X$ has only finitely many singular points $x_1,x_2, \ldots,x_n$. To be more ...

Let $\pi: X\to Y$ be an Iitaka fibration of projective varieties $X,Y$, then is there always the following decomposition $$K_Y+\frac{1}{m!}\pi_*\mathcal O_X(m!K_{X/Y})=P+N$$ where $P$ is ...

Let $f:X\to Y $ be a proper surjective holomorphic fibre space where $X,Y $ are projective varieties. If the central fibre $X_0$ has at worst log terminal singularities, then can we say that all ...