arXiv subjects
Publications and source records attributed to Osamu Fujino.
We discuss the ascending chain condition for lengths of extremal rays. We prove that the lengths of extremal rays of $n$-dimensional $\mathbb Q$-factorial toric Fano varieties with Picard number one satisfy the ascending chain condition.
This paper is an announcement of the minimal model theory for log surfaces in all characteristics and contains some related results including a simplified proof of the Artin-Keel contraction theorem in the surface case.
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 semi-ample if and only if so is the log canonical divisor of its normalization. We also treat many other applications.
We treat Kollár's injectivity theorem from the analytic (or differential geometric) viewpoint. More precisely, we give a curvature condition which implies Kollár type cohomology injectivity theorems. Our main theorem is formulated for a compact Kähler manifold, but the proof uses the space of harmonic forms on a Zariski open set with a suitable complete Kähler metric. We need neither covering tricks, desingularizations, nor Leray's spectral sequence.
We treat a relative version of the main theorem in my previous paper: A transcendental approach to Kollár's injectivity theorem. More explicitly, we give a curvature condition that implies Kollár type cohomology injectivity theorems in the relative setting. To carry out this generalization, we use the Ohsawa-Takegoshi twisted version of Nakano's identity.
We give an alternative proof of Kovács' vanishing theorem. Our proof is based on the standard arguments of the minimal model theory. We do not need the notion of Du Bois pairs. We reduce Kovács' vanishing theorem to the well-known relative Kawamata--Viehweg--Nadel vanishing theorem.
We consider a smooth projective surjective morphism between smooth complex projective varieties. We give a Hodge theoretic proof of the following well-known fact: If the anti-canonical divisor of the source space is nef, then so is the anti-canonical divisor of the target space. We do not use mod $p$ reduction arguments. In addition, we make some supplementary comments on our paper: On images of weak Fano manifolds.
We give a method to investigate isolated log canonical singularities with index one which are not log terminal. Our method depends on the minimal model program. One of the main purposes is to prove that our invariant coincides with Ishii's Hodge theoretic invariant.
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 usual framework of the log minimal model theory.
We reformulate base point free theorems. Our formulation is flexible and has some important applications. One of the main purposes of this paper is to prove a generalization of the base point free theorem in Fukuda's paper: On numerically effective log canonical divisors.
We consider various definitions of non-lc ideal sheaves -- generalizations of the multiplier ideal sheaf which define the non-lc (non-log canonical) locus. We introduce the maximal non-lc ideal sheaf and intermediate non-lc ideal sheaves and consider the restriction theorem for these ideal sheaves. We also begin the development of the theory of a characteristic p>0 analog of maximal non-lc ideals, utilizing some recent work of Blickle.
We give a sufficient condition for the termination of flips. Then we discuss a semi-stable minimal model program for varieties with (numerically) trivial canonical divisor as an application. We also treat a slight refinement of dlt blow-ups.
We consider a canonical bundle formula for generically finite proper surjective morphisms and obtain subadjunction formulae for minimal log canonical centers of log canonical pairs. We also treat related topics and applications.
In this paper, we prove the cone theorem and the contraction theorem for pairs $(X, B)$, where $X$ is a normal variety and $B$ is an effective $\mathbb R$-divisor on $X$ such that $K_X+B$ is $\mathbb R$-Cartier.
We consider a smooth projective morphism between smooth complex projective varieties. If the source space is a weak Fano (or Fano) manifold, then so is the target space. Our proof is Hodge theoretic. We do not need mod $p$ reduction arguments. We also discuss related topics and questions.
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 obtain the cone theorem for log canonical pairs. We do not need Ambro's theory of quasi-log varieties.
We prove that every smooth projective variety with maximal Albanese dimension has a good minimal model. We also treat Ueno's problem on subvarieties of Abelian varieties.
This paper is a gentle introduction to the theory of quasi-log varieties by Ambro. We explain the fundamental theorems for the log minimal model program for log canonical pairs. More precisely, we give a proof of the base point free theorem for log canonical pairs in the framework of the theory of quasi-log varieties.