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Osamu Fujino

Publications and source records attributed to Osamu Fujino.

118 records · Page 7Linked to original sources
arXiv2004

Introduction to the toric Mori theory

The main purpose of this paper is to give a simple and non-combinatorial proof of the toric Mori theory. Here, the toric Mori theory means the (log) Minimal Model Program (MMP, for short) for toric varieties. We minimize the arguments on fans and their decompositions. We recommend this paper to the following people: (A) those who are uncomfortable with manipulating fans and their decompositions, (B) those who are familiar with toric geometry but not with the MMP. People in the category (A) will be relieved from tedious combinatorial arguments in several problems. Those in the category (B) will discover the potential of the toric Mori theory. As applications, we treat the Zariski decomposition on toric varieties and the partial resolutions of non-degenerate hypersurface singularities. By these applications, the reader will learn to use the toric Mori theory.

math.AG↗
arXiv2003

Higher direct images of log canonical divisors and positivity theorems

In this paper, we investigate higher direct images of log canonical divisors. After we reformulate Kollár's torsion-free theorem, we treat the relationship between higher direct images of log canonical divisors and the canonical extensions of Hodge filtration of gradedly polarized variations of mixed Hodge structures. As a corollary, we obtain a logarithmic version of Fujita-Kawamata's semi-positivity theorem. By this semi-positivity theorem, we generalize Kawamata's positivity theorem and apply it to the study of a log canonical bundle formula. The final section is an appendix, which is a result of Morihiko Saito.

math.AG↗
arXiv2002

Remarks on algebraic fiber spaces

In this paper, we collect basic properties of the Albanese dimension and explain how to generalize the main theorem of [F2](math.AG/0204262). This paper is a supplement and a generalization of [F2]. We also prove an inequality of irregularities for algebraic fiber spaces in the appendix, which is an exposition of Fujita-Kawamata's semi-positivity theorem.

math.AG↗
arXiv2001

Notes on toric varieties from Mori theoretic viewpoint

The main purpose of this notes is to supplement the paper reid, which treated Minimal Model Program (also called Mori's Program) on toric varieties. We calculate lengths of negative extremal rays of toric varieties. As an application, we obtain a generalization of Fujita's conjecture for singular toric varieties. We also prove that every toric variety has a small projective toric $\bQ$-factorialization.

math.AG↗
arXiv1999

The indices of log canonical singularities

Let $(P\in X,Δ)$ be a three dimensional log canonical pair such that $Δ$ has only standard coefficients and $P$ is a center of log canonical singularities for $(X,Δ)$. Then we get an effective bound of the indices of these pairs and actually determine all the possible indices. Furthermore, under certain assumptions including the log Minimal Model Program, an effective bound is also obtained in dimension $n\geq 4$.

math.AG↗
arXiv1999

Applications of Kawamata's positivity theorem

In this paper we treat some applications of Kawamata's positivity theorem. We get a weak answer to \cite [Section 3]{KeMaMc}. And we investigate the singularities on the target spaces of some morphisms.

math.AG↗
arXiv1999

Base point free theorem of Reid-Fukuda type

Let $(X,Δ)$ be a proper dlt pair and $L$ a nef Cartier divisor such that $aL-(K_X+Δ)$ is nef and log big on $(X,Δ)$ for some $a\in {\mathbb Z}_{>0}$. Then $|mL|$ is base point free for every $m\gg 0$.

math.AG↗