On log canonical divisors that are log quasi-numerically positive

Let $(X, \Delta)$ be a four-dimensional log variety that is projective over the field of complex numbers. Assume that $(X, \Delta)$ is not Kawamata log terminal (klt) but divisorial log terminal (dlt). First we introduce the notion of "log quasi-numerically positive", by relaxing that of "numerically positive". Next we prove that, if the log canonical divisor $K_X + \Delta$ is log quasi-numerically positive on $(X, \Delta)$ then it is semi-ample.Comment: 4 pages, LaTeX2e, the published versio

A Base Point Free Theorem of Reid Type, II

Let $X$ be a complete algebraic variety over {\bf C}. We consider a log variety $(X,\Delta)$ that is weakly Kawamata log terminal. We assume that $K_X+\Delta$ is a {\bf Q}-Cartier {\bf Q}-divisor and that every irreducible component of $\lfloor \Delta \rfloor$ is {\bf Q}-Cartier. A nef and big Cartier divisor $H$ on $X$ is called {\it nef and log big} on $(X,\Delta)$ if $H |_B$ is nef and big for every center $B$ of non-"Kawamata log terminal" singularities for $(X,\Delta)$. We prove that, if $L$ is a nef Cartier divisor such that $aL-(K_X+\Delta)$ is nef and log big on $(X,\Delta)$ for some $a \in$ {\bf N}, then the complete linear system $| mL |$ is base point free for $m \gg 0$.Comment: AMS-TeX v2.1, 8 pages, note new e-mail address on the 1st page of the manuscrip

The Study for the Tax System of Cross-border Corporate Reorganizations : Focusing on the EU Merger Tax Directive for Considering the Future Direction in Japan

This article concludes that the legal framework of the EU Merger Tax Directive (hereinafter; MTD) can be an option other than the legal framework of cross-border corporate reorganizations in U.S. tax law as the future direction for the tax system of cross-border corporate reorganizations in Japan (hereinafter; TSCCR). From this study, it followed that the TSCCR in Japan had five issues: (1) Lack of the criterion for applying the TSCCR in Japan; (2) Inadequacy of the definition of qualified corporate reorganizations covered; (3) Inadequacy of the definition of persons covered; (4) Inadequacy of tax deferral requirements; (5) Lack of the anti-tax abuse provision. Based on each implication, this article recommends some amendments to the TSCCR in Japan. It\u27s also worth noting that this article will be expected to bring not only the trigger of arguments for the TSCCR in Japan as academic significance, but also the prospective increase of inbound investment in Japan through cross-border corporate reorganizations as social significance.This work was supported by JSPS KAKENHI Grant Number JP16K03312