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Osamu Fujino

Publications and source records attributed to Osamu Fujino.

At least 19 recordsLinked to original sources
arXiv2026

Characteristic-free characterizations of projective space for smooth toric varieties

We prove that a smooth projective toric variety over an algebraically closed field of arbitrary characteristic is isomorphic to a projective space if its tangent bundle contains an ample locally free subsheaf of positive rank. No torus-equivariant structure on this subsheaf is assumed. The proof uses primitive relations, the toric Euler sequence, and characteristic-free cohomological lifting. As an application of the same method, we establish the toric form of Beauville's cohomological characterization of projective spaces and quadrics, including the polarization. Without the toric hypothesis, both characterizations fail in characteristic two.

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arXiv2026

An affine local criterion for toric projective space bundles

We study when an equidimensional toric morphism is forced to be a projective-space bundle. Our main result is an affine rigidity theorem: if the base space is affine, the toric relative canonical divisor is $\mathbb Q$-Cartier, and its negative has degree greater than the relative dimension on every complete curve, then the morphism is equivariantly a trivial projective-space bundle. As an application, we derive a projective-space-bundle theorem for equidimensional toric contractions associated to long extremal rays, without assuming $\mathbb Q$-factoriality.

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arXiv2026

On finiteness of relative log pluricanonical representations

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 existence of log canonical flips for complex analytic spaces. Roughly speaking, we reduce the abundance conjecture for semi-log canonical pairs to the case of log canonical pairs in the complex analytic setting. Moreover, we show that the abundance conjecture for projective morphisms of complex analytic spaces can be reduced to the classical abundance conjecture for projective varieties.

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arXiv2026

Notes on rational chain connectedness

We extend Hacon--M\textsuperscript{c}Kernan's rational chain connectedness theorem to the complex analytic setting. As a consequence, we prove that the fibers of any resolution of singularities of complex analytic kawamata log terminal singularities are rationally chain connected. In contrast to the original approach, we avoid the use of extension theorems and instead rely on the minimal model program.

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arXiv2026

Non-projective complete log canonical surfaces

We construct non-projective complete log canonical algebraic surfaces whose canonical divisors are semi-ample over an algebraically closed field of any characteristic other than the algebraic closure of a finite field. We provide a unified framework to construct such surfaces for any given non-negative Kodaira dimension, namely, zero, one, or two. Furthermore, we show that any complete log canonical algebraic surface with Kodaira dimension minus infinity is automatically projective. This projectivity result confirms that our construction covers all possible values for the Kodaira dimension of non-projective complete log canonical surfaces.

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arXiv2026

Notes on acceptable bundles I

The notion of acceptable bundles plays a fundamental role in the Simpson--Mochizuki theory. This paper presents a detailed study of acceptable bundles on a punctured disk. In addition to its expository aspects, we introduce a new invariant and provide arguments that differ from those of Simpson and Mochizuki.

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arXiv2026

Notes on acceptable bundles II

The notion of acceptable bundles plays a fundamental role in the Simpson--Mochizuki theory. We study acceptable bundles on a partially punctured polydisk in detail. While this article is primarily expository, it also presents new arguments that differ from those of Mochizuki.

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arXiv2025

On a vanishing theorem for surfaces

We propose a new formulation of a vanishing theorem for surfaces. Although this vanishing theorem follows easily from the well-known Kawamata--Viehweg vanishing theorem, it turns out to be remarkably useful. In particular, it is sufficient for the minimal model theory of log surfaces, and it allows one to carry out both the minimal model program and the abundance theorem for log surfaces without invoking any of the deeper vanishing theorems.

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arXiv2025

On non-projective complete toric varieties

For every complete toric variety, there exists a projective toric variety which is isomorphic to it in codimension one. In this paper, we show that every smooth non-projective complete toric threefold of Picard number at most five becomes projective after a finite succession of flops or anti-flips.

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arXiv2025

Variation of mixed Hodge structure and its applications

We discuss variations of mixed Hodge structure arising from projective morphisms of complex analytic spaces. Then we treat generalizations of Kollár's torsion-free theorem, vanishing theorem, and so on, for reducible complex analytic spaces as an application. The results will play a crucial role in the theory of minimal models for projective morphisms between complex analytic spaces.

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arXiv2025

On toric foliated pairs

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

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arXiv2025

On quasi-log structures for complex analytic spaces

We introduce the notion of quasi-log complex analytic spaces and establish various fundamental properties. Moreover, we prove that a semi-log canonical pair naturally has a quasi-log complex analytic space structure. This paper is part of the author's project to establish a minimal model theory for projective morphisms between complex analytic spaces.

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arXiv2024

On quasi-Albanese maps

We discuss Iitaka's theory of quasi-Albanese maps in details. We also give a detailed proof of Kawamata's theorem on the quasi-Albanese maps for varieties of the logarithmic Kodaira dimension zero. Note that Iitaka's theory is an application of Deligne's mixed Hodge theory for smooth algebraic varieties.

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arXiv2024

A remark on toric foliations

If a toric foliation on a projective Q-factorial toric variety has an extremal ray whose length is longer than the rank of the foliation, then the associated extremal contraction is a projective space bundle and the foliation is the relative tangent sheaf of the extremal contraction.

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arXiv2023

Positivity of extensions of vector bundles

In this paper, we study when positivity conditions of vector bundles are preserved by extension. We prove that an extension of a big (resp. pseudo-effective) line bundle by an ample (resp. a nef) vector bundle is big (resp. pseudo-effective). We also show that an extension of an ample line bundle by a big line bundle is not necessarily pseudo-effective. In particular, this implies that an almost nef vector bundle is not necessarily pseudo-effective.

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