Related papers: Minimal model theory for log surfaces

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…

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…

We introduce the notion of generalized MR log canonical surfaces and establish the minimal model theory for generalized MR log canonical surfaces in full generality.

We establish the minimal model theory for $\mathbb Q$-factorial log surfaces and log canonical surfaces in Fujiki's class $\mathcal C$.

We discuss the relationship among various conjectures in the minimal model theory including the finite generation conjecture of the log canonical rings and the abundance conjecture. In particular, we show that the finite generation…

This paper is an announcement of the minimal model theory for log surfaces in all characteristics and contains some related results including a simplified proof of the Artin-Keel contraction theorem in the surface case.

We establish the minimal model program for log canonical and Q-factorial surfaces over excellent base schemes.

We prove that the class of log canonical rational singularities is closed under the basic operations of the minimal model program. We also give some supplementary results on the minimal model program for log canonical surfaces.

We show that minimal models of log canonical pairs exist, assuming the existence of minimal models of smooth varieties.

We propose a new formulation of a vanishing theorem for surfaces. Although this vanishing theorem follows easily from the well-known Kawamata--Viehweg vanishing theorem, it turns out to be remarkably useful. In particular, it is sufficient…

In this paper, we show the abundance theorem for log canonical surfaces over fields of positive characteristic.

Under the assumption of the minimal model theory for projective klt pairs of dimension $n$, we establish the minimal model theory for lc pairs $(X/Z,\Delta)$ such that the log canonical divisor is relatively log abundant and its restriction…

Fujino and Tanaka established the minimal model theory for $\mathbb Q$-factorial log surfaces in characteristic $0$ and $p$, respectively. We prove that every intermediate surface has only log terminal singularities if we run the minimal…

We treat two different topics on the log minimal model program, especially for four-dimensional log canonical pairs. (a) Finite generation of the log canonical ring in dimension four. (b) Abundance theorem for irregular fourfolds. We obtain…

We show the finiteness of log pluricanonical representations under the assumption of the existence of a good minimal model.

We prove that many of the results of the LMMP hold for $3$-folds over fields of characteristic $p>5$ which are not necessarily perfect. In particular, the existence of flips, the cone theorem, the contraction theorem for birational extremal…

We prove that a log surface has only finitely many weakly log canonical projective models with klt singularities up to log isomorphism, by reducing the problem to the boundedness of their polarization.

We prove the abundance theorem for log canonical $n$-folds such that the boundary divisor is big assuming the abundance conjecture for log canonical $(n-1)$-folds. We also discuss the log minimal model program for log canonical $4$-folds.

We prove that the canonical ring of a smooth projective variety is finitely generated.

Varieties with log terminal and log canonical singularities are considered in the Minimal Model Program, see \cite{...} for introduction. In \cite{shokurov:hyp} it was conjectured that many of the interesting sets, associated with these…