Related papers: Adjoint rings are 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.
We prove the finite generation of the adjoint ring for $\mathbb{Q}$-factorial log surfaces over any algebraically closed field.
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 finite generation of canonical rings of projective variety of general type defined over complex numbers.
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…
An introduction to all the key ideas of Lazic's proof of the theorem on the finite generation of adjoint rings.
We prove that the log canonical ring of a projective log canonical pair in Kodaira dimension two is finitely generated.
We give a light introduction to some recent developments in Mori theory, and to our recent direct proof of the finite generation of the canonical ring.
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…
We find necessary and sufficient conditions for the finite separability of monogenic rings. As a corollary, we prove that a finitely generated torsion-free PI-ring is finitely separable if and only if its additive group is finitely…
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 prove two approximations of the open problem of whether the adjoint group of a non-nilpotent nil ring can be finitely generated: We show that the adjoint group of a non-nilpotent Jacobson radical cannot be boundedly generated, and on the…
The log canonical ring of a projective plt pair with the Kodaira dimension two is finitely generated.
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 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…
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 obtain a correct generalization of Shokurov's non-vanishing theorem for log canonical pairs. It implies the base point free theorem for log canonical pairs. We also prove the rationality theorem for log canonical pairs. As a corollary,…
We prove the existence of good minimal models for any klt algebraically integrable adjoint foliated structure of general type, and that Fano algebraically integrable adjoint foliated structures with total minimal log discrepancies and…
This paper deals with some results concerning finitely generated coreduced comultiplication modules over a commutative ring.