9 problems

Let $n\geq 5$. For a smooth projective $n$-fold $X$ of general type, write $h^{2,0}(X)$ for the dimension of its space of global holomorphic two-forms, and let $r_{n-2}$ denote the…

Relative canonical stability conjecture. The $n$-th relative canonical stability satisfies

Let $Y$ be a smooth projective threefold of general type. The $m$-th pluricanonical map of $Y$ is the map defined by the $m$-th pluricanonical linear system. Demailly's conjecture.…

Fix a complex projective variety $X$, and let ${\cal G}_m$ be the set of nonsingular complex projective varieties $Y$ for which the $m$-th pluricanonical map…

Let $X$ be a minimal variety of general type of dimension $n$ with at worst $\mathbb{Q}$-factorial terminal singularities, and suppose that its canonical divisor $K_X$ is Cartier.…

For each positive integer $n$, let $r_n$ be an integer such that the pluricanonical maps of smooth projective varieties of general type and dimension $n$ are birational for all…

Let $X$ be a variety of large volume and dimension $n$, and let $r_n$ denote an integer such that pluricanonical maps of smooth projective varieties of general type and dimension…

Let $X$ be a minimal projective $3$-fold of general type, and let $p_g(X)$ denote its geometric genus. Write $\varphi_{14,X}$ for the rational map defined by the complete linear sy…

Let $n\geq 5$ be an integer, let $K(n)>0$ be a constant, and let $X$ be a smooth projective $n$-fold. Write $\operatorname{vol}(X)$ for its canonical volume, $\varphi_{m,X}$ for th…