Related papers: Existence of minimal models for varieties of log g…
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 show that minimal models of log canonical pairs exist, assuming the existence of minimal models of smooth varieties.
We prove that the log canonical ring of a projective log canonical pair in Kodaira dimension two is finitely generated.
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 non-vanishing conjecture and the log minimal model conjecture for projective log canonical pairs can be reduced to the non-vanishing conjecture for smooth projective varieties such that the boundary divisor is zero.
This paper proves finite generation of the log canonical ring without Mori theory.
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 prove the existence of pl-flips.
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 that the canonical ring of a canonical variety in the sense of de Fernex and Hacon is finitely generated. We prove that canonical varieties are klt if and only if R(-K_X) is finitely generated. We introduce a notion of nefness for…
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 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 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.
We prove that a log surface has only finitely many weakly log canonical projective models with klt singularities up to log isomorphism, by reducing the problem to the boundedness of their polarization.
The log canonical ring of a projective plt pair with the Kodaira dimension two is finitely generated.
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 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…
In this article we prove, in a simple way, that for any complete toric variety, and for any Cartier divisor, the ring of global sections of multiples of the line bundle associated to the divisor is finitely generated.
We determine the minimal possible volume of a projective log canonical surface of general type with prescribed positive geometric genus. As applications, we provide effecitive Noether type inequalities for log canonical threefolds and…