The main purpose of this paper is to make Nakayama’s theorem more accessible. We give a proof of Nakayama’s theorem based on the negative definiteness of intersection matrices of exceptional curves. In this paper, we treat Nakayama’s theorem on algebraic varieties over any algebraically closed field of arbitrary characteristic although Nakayama’s original statement is formulated for complex analytic spaces.

Serrrano's Conjecture says that if $L$ is a strictly nef line bundle on a smooth projective variety $X$, then $K_X+tL$ is ample for $ t > dim X+1$. In this paper I will prove a few cases of this… Expand

Our main goal in this article is to establish a quantitative version of the positivity properties of twisted relative pluricanonical bundles and their direct images. The notion of "singular Hermitian… Expand

Abstract We give an ampleness criterion of a torsion free coherent sheaf at a given point in terms of a curvature positivity of a singular Hermitian metric.

Let X$X$ be a smooth connected projective manifold, together with an snc orbifold divisor Δ$\Delta $, such that the pair (X,Δ)$(X, \Delta )$ is log-canonical. If KX+Δ$K_{X}+\Delta $ is… Expand