Zariski decomposition and canonical rings of elliptic threefolds
Zariski decomposition and canonical rings of elliptic threefolds
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Zariski 分解和椭圆三重的正则环
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发表时间：
1986
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通讯作者：
T. Fujita
中科院分区：
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作者：
T. Fujita
$Oplus_{t}{}_{geq0}H^{0}(M，IK_{M})$，称为$M$的典范环。特别地，我们将证明这是有限生成的(见下面的(3.5))。正如我们在[F4]中概述的那样，我们进行如下操作。S 1致力于高维Zariski分解的理论(参见[Z]、[F1])。在S 2中，我们给出了椭圆纤维空间的Kodaira-Ueno型正则丛公式。[KOL]，[U1]))。在S 3中，我们结合这两个理论，借助于[F5]中关于曲面的“分数对数”正则环的一个结果证明了主要定理。在附录中，我们从Zariski分解的观点考虑一般类型的流形的情况。
$oplus_{t}{}_{geqq 0}H^{0}(M, iK_{M})$ , which is called the canonical ring of $M$. In particular we will prove that this is finitely generated (see (3.5) below). As we outlined in [F4], we proceed as follows. S 1 is devoted to a theory of Zariski decomposition in higher dimensions (cf. [Z], [F1]). In S 2 we present a canonical bundle formula of Kodaira-Ueno type for elliptic fiber spaces (cf. [Kol], [U1]). In S 3, combining these two theories, we prove the main theorem with the help of a result in [F5] concerning “fractionally logarithmic” canonical rings of surfaces. In the Appendix we consider the case of manifolds of general type from the view point of Zariski decomposition.