相关论文: On the log canonical ring in Kodaira dimension two

We prove the finiteness of log pluricanonical representations for projective log canonical pairs with semi-ample log canonical divisor. As a corollary, we obtain that the log canonical divisor of a projective semi log canonical pair is…

We apply the theory of cotorsion pairs to study closure properties of classes of modules with finite projective dimension with respect to direct limit operations and to filtrations. We also prove that if the ring is an order in an…

We show some inductive statements for the index conjecture for log canonical Calabi-Yau pairs. Using it, we show that boundedness of log canonical index for log canonical Calabi Yau pairs with rational DCC coefficients in dimension 3. We…

We prove that a projective semistable morphism of fs log analytic spaces yields polarized log Hodge structures in the canonical way.

We prove the finite generation of the adjoint ring for $\mathbb{Q}$-factorial log surfaces over any algebraically closed field.

We generalise two facts about finite dimensional algebras to finite dimensional differential graded algebras. The first is the Nakayama Lemma and the second is that the simples can detect finite projective dimension. We prove two dual…

We prove the effectiveness of the log Iitaka fibration in Kodaira codimension two for varieties of dimension$\le 4$. In particular, we finish the proof of effective log Iitaka fibration in dimension two. Also, we show that for the log…

We prove the Kodaira vanishing theorem for log-canonical and semi-log-canonical pairs. We also give a relative vanishing theorem of Reid--Fukuda type for semi-log-canonical pairs.

Let $\kk$ be an algebraically closed field of characteristic zero and $\KK$ a finitely generated field over $\kk$. Let $\Sigma$ be a central simple $\KK$-algebra, $X$ a normal projective model of $\KK$ and $\Lambda$ a sheaf of maximal…

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 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 paper, we prove the non-vanishing and some special cases of the abundance for log canonical threefold pairs over an algebraically closed field $k$ of characteristic $p > 3$. More precisely, we prove that if $(X,B)$ be a projective…

We show that log canonical thresholds of fixed dimension are standardized. More precisely, we show that any sequence of log canonical thresholds in fixed dimension $d$ accumulates in a way which is i) either similar to how standard and…

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 lengths of extremal rational curves, Fujita's freeness, and the Kodaira vanishing theorem for log canonical toric foliated pairs.

We prove an additivity result for the log Kodaira dimension of algebraic fiber spaces over abelian varieties, a superadditivity result for fiber spaces over varieties of maximal Albanese dimension, as well as a subadditivity result for log…

We construct a moduli space of stable projective pairs with a nontrivial action of a connected reductive group. These stable reductive pairs are higher-dimensional analogs of stable n-pointed curves and generalize to the non-commutative…

We prove that the ascending chain condition (ACC) for log canonical (lc) thresholds in dimension $d$ and Special Termination in dimension $d$ imply the termination of any sequence of log flips starting with a $d$-dimensional lc pair of…

This paper deals with some results concerning finitely generated coreduced comultiplication modules over a commutative ring.

We prove that the log Iitaka conjecture holds for log canonical fibrations when log canonical divisor of a sufficiently general fiber is abundant.