Related papers: Fujita-type freeness for quasi-log canonical three…

We prove Fujita-type basepoint-freeness for projective quasi-log canonical curves and surfaces.

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…

We show that Fujita's conjecture is true for quasi-elliptic surfaces. Explicitly, for any quasi-elliptic surface $X$ and an ample line bundle $A$ on $X$, we have $K_X + tA$ is base point free for $t \geq 3$ and is very ample for $t \geq 4$.

Let X be a smooth complex projective variety of dimension n. We prove bounds on Fujita's basepoint freeness conjecture that grow as nloglog(n).

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 generalize the result of Kawamata concerning the strong version of Fujita's freeness conjecture for smooth 3-folds to some singular cases, namely, Gorenstein terminal singularities and quotient singularities of type 1/r(1,1,1) and of…

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…

We introduce various new operations for quasi-log structures. Then we prove the basepoint-free theorem of Reid--Fukuda type for quasi-log schemes as an application.

We show Fujita's spectrum conjecture for $\epsilon$-log canonical pairs and Fujita's log spectrum conjecture for log canonical pairs. Then, we generalize the pseudo-effective threshold of a single divisor to multiple divisors and establish…

Let $(X,L)$ be a quasi-polarized canonical Calabi-Yau threefold. In this note, we show that $\vert mL\vert$ is basepoint free for $m\geq 4$. Moreover, if the morphism $\Phi_{\vert 4L\vert}$ is not birational onto its image and $h^0(X,L)\geq…

We prove that the pull-back of a quasi-log scheme by a smooth quasi-projective morphism has a natural quasi-log structure. We treat an application to log Fano pairs. This paper also contains a proof of the simple connectedness of log Fano…

In this note we establish a new Fujita-type effective bound for the base point freeness of adjoint line bundles on a compact complex projective manifold of complex dimension $n$. The bound we obtain (approximately) differs from the linear…

Fujita's conjecture is known to be false in positive characteristic. We conjecture and give an approach to a new variant of Fujita's conjecture for the basepoint-freeness, very ampleness, and jet ampleness of linear systems of the form…

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 prove Koll\'ar-type effective basepoint-free theorems for quasi-log canonical pairs.

We consider Fujita's freeness conjecture in a relative setting and prove a criterion by proving a correct Q-divisor version of the Kollar vanishing theorem.

In this paper, we show how to prove the basepoint-freeness for linear systems on irregular varieties inductively. For instance, we prove that Fujita's conjecture holds for irregular varieties of dimension $\mathnormal{n}$ with a nef…

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.

The authors and D. Martinelli proved 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. In this paper, we drop the bigness condition…

The result on 3-fold is now optimal by the result of Ein-Lazarsfeld and Helmke.