Related papers: The Minimal Model Program Revisited
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.
This paper is the first of two steps in a project to prove finite generation of the log canonical ring without Mori theory.
The purpose of this note is to review an algebraic proof of the finite generation theorem due to Birkar-Cascini-Hacon-McKernan whose method is based on the Minimal Model Program. A survey article for Current Development in Mathematics 2007.
We prove the finite generation of canonical rings of projective variety of general type defined over complex numbers.
We prove that the finite generation of adjoint rings proved in [Cascini and Lazi\'c] implies all the foundational results of the Minimal Model Program: the Rationality, Cone and Contraction theorems, the existence of flips, and termination…
We prove that the canonical ring of a smooth projective variety is finitely generated.
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…
There are two main examples where a version of the Minimal Model Program can, at least conjecturally, be performed successfully: the first is the classical MMP associated to the canonical divisor, and the other is Mori Dream Spaces. In this…
In this paper, we discuss a proof of existence of log minimal models or Mori fibre spaces for klt pairs $(X/Z,B)$ with $B$ big$/Z$. This then implies existence of klt log flips, finite generation of klt log canonical rings, and most of the…
This paper proves finite generation of the log canonical ring without Mori theory.
This set of notes provides some additional explanatory material on the analytic proof of the finite generation of the canonical ring for a compact complex algebraic manifold of general type.
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 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…
The first aim of this note is to give a concise, but complete and self-contained, presentation of the fundamental theorems of Mori theory - the nonvanishing, base point free, rationality and cone theorems - using modern methods of…
The main results of this paper are already known (V.V. Shokurov, the non-vanishing theorem, 1985). Moreover, the non-$\mathbb{Q}$-factorial MMP was more recently considered by O~Fujino, in the case of toric varieties (Equivariant…
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.
The main purpose of this notes is to supplement the paper reid, which treated Minimal Model Program (also called Mori's Program) on toric varieties. We calculate lengths of negative extremal rays of toric varieties. As an application, we…
We treat equivariant completions of toric contraction morphisms as an application of the toric Mori theory. For this purpose, we generalize the toric Mori theory for non-$\mathbb Q$-factorial toric varieties. So, our theory seems to be…
We prove two theorems on the locally finite decompositions of the cones of divisors by the cones which correspond to canonical and minimal models. We introduce the concept of the numerical linear systems in order to simplify the argument on…
We display a new family of prime ideals with unbounded minimal number of generators in a three-dimensional power series ring over a field of characteristic zero. These primes are obtained as the kernel of a quasi-monomial algebra…