10 problems

Let $X$ be a compact complex manifold of complex dimension $n$, and let $L$ be an ample holomorphic line bundle on $X$. Fujita's conjecture. The line bundle…

Let $f:X\to Y$ be a surjective morphism between smooth projective varieties with $\dim Y=n$, let $\mathcal L$ be any ample invertible sheaf on $Y$, and let $k$ be a positive intege…

Uniform moving-Seshadri-constant conjecture. There exist integer-valued functions $c(n)$ and $d(n)$ and a real-valued function $e(n)$, all depending only on $n$, such that

Fujita-type jet-ampleness conjecture. There exist integer-valued polynomial functions $a_\ell(n)$ and $b_\ell(n)$ depending only on $n$ such that

Helmke's numerical Fujita freeness conjecture. Under these conditions, the adjoint divisor

Let $X$ be a smooth projective variety and let $L$ be a line bundle on $X$. For every proper subvariety $Z\varsubsetneq X$, write $(L^{\dim Z}.Z)$ for the intersection number of…

Let $f:X\to Y$ be a surjective morphism of smooth projective varieties over an algebraically closed field of characteristic zero, with $Y$ of dimension $n$, and let $\mathcal L$ be…

Let $X$ and $Y$ be smooth projective varieties, let $\pi\colon X\to Y$ be a smooth fibration, and let $f_X$, $f_Y$, and $f_\pi$ denote the corresponding Fujita numbers. Fujita-numb…

The pointwise base-point-freeness conjecture. The adjoint line bundle $K_Y+L$ is base point free at $y$. The source presents this as a known generalization of Fujita's base point f…

For a smooth polytope ${\mathcal P}$ associated with an $n$-dimensional toric variety, let $b{\mathcal P}$ be called large when…