Osamu Fujino’s research while affiliated with Kyoto University and other places

... Although they may look artificial and technical, they are very useful and indispensable for the study of varieties and pairs whose singularities are worse than Kawamata log terminal (see [1;12,Chap. 6;15,16,19,20] and so on). In [18], we showed that Theorems 1.8 and 1.9 follow from Theorem 1.7 (i) and (ii). ...

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Variation of mixed Hodge structure and its applications

... We make an important remark on Lemma 3. [3,Lemma 3.14]) easily follows from [3, Theorem 1.1], which is [3, Theorem 3.1]. We note that we use Lemma 3 (see [3,Lemma 3.14]) in the proof of [3,Theorem 3.1] in [3,Section 3]. ...

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Correction: On quasi-Albanese maps

... The present paper aims to address a missing component of the minimal model program for projective morphisms between complex analytic spaces (see [Fuj12], [Fuj13], [Fuj14], [Fuj15], [Fuj17], [FF], [DHP], [EH2], [LM], [EH3], [H5], and others). Broadly speaking, this work can be viewed as a complex analytic generalization of [FG] (see also [Fuj1]). ...

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On finiteness of relative log pluricanonical representations

... This paper is a continuation of [FjS2] and is obviously a generalization of [Fj1]. Throughout this paper, we will work over C, the field of complex numbers. ...

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On toric foliated pairs

... We make a small remark on [EjFI] for the reader's convenience. Professor Robert Lazarsfeld pointed out that the following example answers [EjFI,Question 3.2] negatively. ...

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On the Kodaira dimension

... By combining Theorem 1.5 with [EH2,Theorem 1.3], we establish the existence of good dlt blow-ups in the complex analytic setting. This result immediately yields the inversion of adjunction for log canonicity (see [Fuj16,Theorem 1.1] and Theorem 6.3). ...

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On finiteness of relative log pluricanonical representations

... Theorem 1.8 is significantly more profound than Theorem 6.1. It can be regarded as a complex analytic version of [FH,Lemma 3.5]. For related results in the original algebraic setting, see [FH]. ...

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On finiteness of relative log pluricanonical representations

... Proposition 9.1 ( [S,Proposition 5.2] and [F15,Proposition 7.1]). Let π : X → S be a projective morphism from a normal Q-factorial variety X onto a scheme S. Let ∆ = i d i ∆ i be an effective R-divisor on X, where the ∆ i 's are the distinct prime components of ∆ for all i, such that ...

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Cone theorem and Mori hyperbolicity

... We have already known that the theory of mixed Hodge structures on cohomology with compact support is very useful in the theory of minimal models for higher-dimensional algebraic varieties (see [10;12,Chaps. 5 and 6;16] and so on). Recently, the first author generalized Let (X, D) be an analytic simple normal crossing pair such that D is reduced and let f : X → Y be a proper surjective morphism onto a smooth complex variety Y . ...

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Variation of mixed Hodge structure and its applications

... Proof. Since ∆ and ω are Q-divisors, we can use [F22a,Theorem 21.4] and the analytic analog of [FG12] instead of [FH23,Corollary 5.2]. Thus, we have the analytic analog of the canonical bundle formula in our situation. ...

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Minimal model program for normal pairs along log canonical locus in complex analytic setting