Related papers: Base point free theorem of Reid-Fukuda type

Let $X$ be a complete algebraic variety over {\bf C}. We consider a log variety $(X,\Delta)$ that is weakly Kawamata log terminal. We assume that $K_X+\Delta$ is a {\bf Q}-Cartier {\bf Q}-divisor and that every irreducible component of…

In this article we present a refinement of the base point free theorem for threefolds in positive characteristic. If $L$ is a nef Cartier divisor of numerical dimension at least one on a projective Kawamata log terminal threefold…

We extend Reider's freeness criterion to normal surfaces of characteristic 0. Let Y be a normal surface. Let D be a nef divisor on Y such that K_Y+D is a Cartier divisor. Let x be a point on Y. If x is a base point of |K_Y+D| and…

Let $(X,D)$ be log canonical pair such $\dim X = 3$ and the divisor $-(K_X + D)$ is nef and big. For a special class of such $(X,D)$'s we prove that the linear system $|-n(K_{X}+D)|$ is free for $n \gg 0$.

Let $(X, \Delta)$ be a projective klt three dimensional pair defined over an algebraically closed field characteristic larger than 5. Let $L$ be a nef and big line bundle on $X$ such that $L-K_X-\Delta$ is big and nef. We show that $L$ is…

We prove a base point free theorem for nef and log big divisors on log canonical surfaces.

We show that if $\mathcal{F}$ is an algebraically integrable foliation on a $\mathbb{Q}$-factorial normal projective variety $X$, $ A, B \geq 0$ are $\mathbb{Q}$-divisors on $X$ with $A$ ample such that $(\mathcal{F}, B)$ is foliated dlt…

We reformulate base point free theorems. Our formulation is flexible and has some important applications. One of the main purposes of this paper is to prove a generalization of the base point free theorem in Fukuda's paper: On numerically…

Let $X$ be a smooth projective variety of dimension $5$ and $L$ be an ample line bundle on $X$. We show that $|K_X + 6L|$ is base-point free.

We prove that if $(X, B+\mathbf{M})$ is a generalized klt pair with $K_X+B+\mathbf{M}_X$ nef and abundant, then $K_X+B+\mathbf{M}_X$ is semiample. More generally, we prove a generalized basepoint free theorem for generalized klt pairs.

We prove Koll\'ar's effective base point free theorem for log canonical pairs.

We prove the base point free theorem for big line bundles on a three-dimensional log canonical projective pair defined over the algebraic closure of a finite field.

We present algorithms for basic computations with monoids in finitely generated abelian groups such as monoid membership testing and computing an element of the conductor ideal. Applying them to Mori dream spaces, we obtain algorithms to…

This treats the base-point-freeness of the adjoint bundles on normal surfaces with a boundary. This is an extension of the non-relative version of the theorem of Ein-Lazarsfeld-Masek and the theorem of Kawachi-Masek.

Let $X$ be a complete normal variety, $B$ an effective $\mathbb{R}$-divisor on $X$, and $D$ a Cartier divisor on $X$. Assume that the pair $(X, B)$ is log terminal. We consider the problem whether $H^0(X, D) \ne 0$ and obtain some results…

We prove the base point free theorem for log canonical foliated pairs of rank one on a Q-factorial projective klt threefold. Moreover, we show abundance in the case of numerically trivial log canonical foliated pairs of rank one in any…

This paper proposes a Fujita-type freeness conjecture for semi-log canonical pairs. We prove it for curves and surfaces by using the theory of quasi-log schemes and give some effective very ampleness results for stable surfaces and semi-log…

Generalising and unifying the known theorems for difference and differential fields, it is shown that for every finite free ${\mathbb S}$-algebra ${\mathcal D}$ over a field $A$ of characteristic zero the theory of ${\mathcal D}$-fields has…

We develop techniques of mimicking the Frobenius action in the study of universal homeomorphisms in mixed characteristic. As a consequence, we show a mixed characteristic Keel's base point free theorem obtaining applications towards the…

Let $\mathbb{Z}^2$ be the two-dimensional integer lattice. For an integer $k\geq 1$, a non-zero lattice point is $k$-free if the greatest common divisor of its coordinates is a $k$-free number. We consider the proportions of $k$-free and…