Related papers: Effective basepoint-free theorem for semi-log cano…
In a first part of this paper, we prove constancy of the canonical graded Betti table among the smooth curves in linear systems on Gorenstein weak Fano toric surfaces. In a second part, we show that Green's canonical syzygy conjecture holds…
We introduce the notion of quasi-log complex analytic spaces and establish various fundamental properties. Moreover, we prove that a semi-log canonical pair naturally has a quasi-log complex analytic space structure. This paper is part of…
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 $n \gg 0$.
1) Assuming log Minimal Model Conjecture, we give a construction of a complete moduli space of stable log pairs of arbitrary dimension generalizing directly the space M_{g,n} of pointed stable curves. Each stable pair has semi log canonical…
The LCS locus is an essential ingredient in the proof of fundamental results of Log Minimal Model Program, such as nonvanishing and base point freeness theorems. We prove in this paper that the LCS locus of a log canonical variety has…
The \emph{canonical degree} of a curve $C$ on a surface $X$ is $K_X\cdot C$. Our main result, is that on a surface of general type there are only finitely many curves with negative self--intersection and sufficiently large canonical degree.…
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…
We discuss the relative log minimal model theory for log surfaces in the analytic setting. More precisely, we show that the minimal model program, the abundance theorem, and the finite generation of log canonical rings hold for log pairs of…
The nonvanishing conjecture for projective log canonical pairs plays a key role in the minimal model program of higher dimensional algebraic geometry. The numerical nonvanishing conjecture considered in this paper is a weaker version of the…
In this paper, we show that general Fano complete intersections over an algebraically closed field of arbitrary characteristics are separably rationally connected. Our proof also implies that general log Fano complete intersections with…
The main purpose of this paper is to establish some useful partial resolutions of singularities for pairs from the minimal model theoretic viewpoint. We first establish the existence of log canonical modifications of normal pairs under some…
We show that the anti-canonical bundle of any $\mathbb Q$-factorial surface is numerically effective if and only if it is pseudo-effective. To prove this, we establish a numerical non-vanishing theorem for surfaces polarized with…
I give a necessary and sufficient condition for a nef and big line bundle in positive characteristic to be semi-ample, and then give two applications: I show that the relative dualizing sheaf of the universal curve is semi-ample, in…
We provide an effective ramification theorem for the ratio of canonical forms of a weakly complete flat front in the hyperbolic three-space. Moreover we give the two applications of this theorem, the first one is to show an analogue of the…
We discuss the log minimal model theory for log surfaces. We show that the log minimal model program, the finite generation of log canonical rings, and the log abundance theorem for log surfaces hold true under assumptions weaker than the…
We discuss the birational geometry of singular surfaces in positive characteristic. More precisely, we establish the minimal model program and the abundance theorem for Q-factorial surfaces and for log canonical surfaces. Moreover, in the…
In this paper, we investigate higher direct images of log canonical divisors. After we reformulate Koll\'ar's torsion-free theorem, we treat the relationship between higher direct images of log canonical divisors and the canonical…
The purpose of this note is to show that the minimal $e$ for which every smooth Fano hypersurface of dimension $n$ contains a free rational curve of degree at most $e$ cannot be bounded by a linear function in $n$ when the base field has…
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…
We prove the Kodaira vanishing theorem for log-canonical and semi-log-canonical pairs. We also give a relative vanishing theorem of Reid--Fukuda type for semi-log-canonical pairs.