Related papers: Remarks on log pluricanonical representations
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 prove the finiteness of relative log pluricanonical representations in the complex analytic setting. As an application, we discuss the abundance conjecture for semi-log canonical pairs within this framework. Furthermore, we establish the…
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 show that minimal models of log canonical pairs exist, assuming the existence of minimal models of smooth varieties.
We give a new proof of the finiteness of B-representations. As a consequence of the finiteness of B-representations and Koll\'ar's gluing theory on lc centers, we prove that the (relative) abundance conjecture for slc pairs is implied by…
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.
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 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 the abundance theorem for log canonical $n$-folds such that the boundary divisor is big assuming the abundance conjecture for log canonical $(n-1)$-folds. We also discuss the log minimal model program for log canonical $4$-folds.
We discuss the birational geometry of singular surfaces in positive characteristic. More precisely, we establish the minimal model program and the abundance theorem for Q-factorial surfaces and for log canonical surfaces. Moreover, in the…
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 finiteness of $B$-representations of generalised log canonical pairs. As a consequence, we prove that, the (relative) abundance for a generalised semi-log canonical pair is implied by the abundance for its normalisation.…
We show that a minimal clone has a nontrivial weakly abelian representation iff it has a nontrivial abelian representation, and that in this case all representations are weakly abelian.
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…
Given a three-dimensional projective log canonical pair over a perfect field of characteristic larger than five, there exists a minimal model program that terminates after finitely many steps.
We define the notion of a minimal affinization of an irreducible representation of $U_q(g)$. We prove that minimal affinizations exist and establish their uniqueness in the rank 2 case.
We prove a stronger version of a termination theorem appeared in the paper "On existence of log minimal models II". We essentially just get rid of the redundant assumptions so the proof is almost the same as in there. However, we give a…
We study relations between the property of being log abundant for lc pairs and the termination of log MMP with scaling. We prove that any log MMP with scaling of an ample divisor starting with a projective dlt pair contains only finitely…
We discuss representations of monogenic functions over very regular groups.
We prove that the canonical ring of a smooth projective variety is finitely generated.