Related papers: Finite generation of a canonical ring
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 prove the finite generation of canonical rings of projective variety of general type defined over complex numbers.
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 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.
In the 80th birthday conference for Professor LU Qikeng in June 2006 I gave a talk on the analytic approach to the finite generation of the canonical ring for a compact complex algebraic manifold of general type. This article is my…
This article is written for the Proceedings of the Conference on Current Developments in Mathematics in Harvard University, November 16-17, 2007. It is an exposition of the analytic proof of the finite generation of the canonical ring for a…
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…
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 is the first of two steps in a project to prove finite generation of the log canonical ring without Mori theory.
On August 5, 2005 in the American Mathematical Society Summer Institute on Algebraic Geometry in Seattle and later in several conferences I gave lectures on my analytic proof of the finite generation of the canonical ring for the case of…
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 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…
In this short note we prove a finite generation result for the coordinate ring of certain affine group schemes over a discrete valuation ring. This may be used to simplify the use of results of Prasad and Yu on quasi-reductive groups by…
An introduction to all the key ideas of Lazic's proof of the theorem on the finite generation of adjoint rings.
We give a proof of the finite generation of the cohomology ring of a finite p-group over F_p by reduction to the case of elementary abelian groups, based on Serre's Theorem on products of Bocksteins.
In this paper, we inspect a relatively unexplored notion of finite generation in semirings, namely semirings in which all congruences are finitely generated. Such semirings are dubbed Congruence Noetherian. After developing sufficient…
Let f be a generically finite morphism from X to Y. The purpose of this paper is to show how the O_Y algebra structure on the push forward of O_X controls algebro-geometric aspects of X like the ring generation of graded rings associated to…
This paper proves finite generation of the log canonical ring without Mori theory.
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…
This paper presents a novel approach to constructing finite generating sets for infinitely generated ideals. By integrating algebraic and computational techniques, we provide a method to identify finite generators, demonstrated through…