Related papers: On the log canonical ring in Kodaira dimension two

The log canonical ring of a projective plt pair with the Kodaira dimension two is finitely generated.

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

We prove that the log canonical ring of a klt pair of dimension $3$ with $\mathbb{Q}$-boundary over an algebraically closed field of characteristic $p>5$ is finitely generated. In the process we prove log abundance for such pairs in the…

We prove the finite generation of canonical rings of projective variety of general type defined over complex numbers.

This paper proves finite generation of the log canonical ring without Mori theory.

We prove the termination of 4-fold log flips for klt pairs of Kodaira dimension $\kappa\ge 2$.

We give a new and self-contained proof of the finite generation of adjoint rings with big boundaries. As a consequence, we show that the canonical ring of a smooth projective variety is finitely generated.

We prove the special termination for log canonical pairs and its generalisation in the context of generalised pairs.

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…

In this paper, we generalize the finiteness of models theorem in [BCHM06] to Kawamata log terminal pairs with fixed Kodaira dimension. As a consequence, we prove that a Kawamata log terminal pair with $\mathbb{R}-$boundary has a canonical…

This paper is the first of two steps in a project to prove finite generation of the log canonical ring without Mori theory.

We prove that the local accumulation complexity of the set of log canonical volumes in dimension $\geq 2$ can be infinite.

Let $(X, \Delta)/U$ be klt pairs and $Q$ be a convex set of divisors. Assuming that the relative Kodaira dimensions are non-negative, then there are only finitely many log canonical models when the boundary divisors varying in a relatively…

We prove that a Kawamata log terminal pair has the canonical model.

Consider modular forms arising from a finite-area quotient of the upper-half plane by a Fuchsian group. By the classical results of Kodaira-Spencer, this ring of modular forms may be viewed as the log spin canonical ring of a stacky curve.…

We study very basic slc-trivial fibrations. We show that restricting on any lc center of a very basic slc-trivial fibration, its moduli part is numerically trivial if and only if it is $\mathbb Q$-linearly trivial. We then prove that…

We prove the Nonvanishing conjecture for uniruled projective log canonical pairs of dimension $n$, assuming the Nonvanishing conjecture for smooth projective varieties in dimension $n-1$. We also show that the existence of good minimal…

We prove the existence of good log minimal models for dlt pairs of numerical log Kodaira dimension 0.

We prove a result on the inversion of adjunction for log canonical pairs that generalizes Kawakita's result to log canonical centers of arbitrary codimension.

Let $(X,B)$ be a log canonical pair over a normal variety $Z$ with maximal Albanese dimension. If $K_X+B$ is relatively abundant over $Z$ (for example, $K_X+B$ is relatively big over $Z$), then we prove that $K_X+B$ is abundant. In…