Related papers: Minimal model program for excellent surfaces

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

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 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 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 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 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.

Given a three-dimensional projective log canonical pair over a perfect field of characteristic larger than five, there exists a minimal model program that terminates after finitely many steps.

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

We show that the Sarkisov program holds for $\mathbb{Q}$-factorial log surfaces and log canonical surfaces over any algebraically closed field.

We establish the minimal model theory for normal pairs along log canonical locus in the complex analytic setting. This is the complex analytic analog of the previous result by the author.

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 prove that one can run the log minimal model program for log canonical $3$-fold pairs in characteristic $p>5$. In particular we prove the Cone Theorem, Contraction Theorem, the existence of flips and the existence of log minimal models…

If $(X, \mcF, \D)$ is a projective rank two foliated log canonical triple such that $(X,B)$ is klt for some $0 \leq B \leq \D$, we show that we can run a $(K_\mcF +\Delta)$-MMP and any such MMP terminates with either a minimal model or Mori…

We study the minimal model program for lc pairs on projective morphism between complex analytic spaces. More precisely, we generalize the results by Birkar and the second author to the setup by Fujino.

We prove the ideal-adic semi-continuity of minimal log discrepancies on surfaces.

We show that minimal models of $\mathbb{Q}$-factorial NQC log canonical generalised pairs exist, assuming the existence of minimal models of smooth varieties. More generally, we prove that on a $\mathbb{Q}$-factorial NQC log canonical…

We prove an existence theorem for good moduli spaces, and use it to construct the second flip in the log minimal model program for the moduli space of stable curves. In fact, our methods give a uniform, self-contained construction of the…

We give a sufficient condition for the termination of flips. Then we discuss a semi-stable minimal model program for varieties with (numerically) trivial canonical divisor as an application. We also treat a slight refinement of dlt…

We classify completely the surfaces of general type whose canonical map is 3-to-1 onto a surface of minimal degree in projective space. These surfaces fall into 5 distinct classes and we give explicit examples belonging to each of these…

We study the termination of minimal model programs for log canonical pairs in the complex analytic setting. By using the termination, we prove a relation between the minimal model theory for projective log canonical pairs and that for log…