On Fermat varieties
On Fermat varieties
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DOI：
10.2748/tmj/1178229881
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发表时间：
1979
影响因子：
0.5
通讯作者：
T. Katsura
中科院分区：
文献类型：
--
作者：
T. Shioda;T. Katsura
X？+x？++x？+ί=0。在本文中，当我们需要指定基域k的特征p时，我们用Xrm或Xrm(P)表示它；我们总是假设m^0(Mod P)。本文的目的是阐明具有共同度和不同维度的Fermat簇的“归纳结构”，并将其应用于关于Fermat簇的单调性和代数环的问题。主要结果如下：定理1.对任意正整数r和S，XZf由乘积Xrm×X8m得到：1)爆破同构于X~x X‘*的子簇，2)取膨胀簇关于m阶循环群作用的商，3)从同构于P×X’ΰ和XLRxP‘的两个子簇的商中爆破。
(0.1) x? + x? + + x?+ί = 0 . Throughout this paper, we denote it by Xrm, or by X r m(p), when we need to specify the characteristic p of the base field k; we always assume that m ^ 0 (mod p). The purpose of this paper is to clarify the "inductive structure" of Fermat varieties of a common degree and of various dimensions, and apply it to the questions concerning the unirationality and algebraic cycles of a Fermat variety. The main results are stated as follows: THEOREM I. For any positive integers r and s, XZf is obtained from the product Xrm x X 8 m by 1) blowing up a subvariety isomorphic to X~ x X'*, 2) taking the quotient of the blown up variety with respect to an action of the cyclic group of order m, and 3) blowing down from the quotient two subvarieties isomorphic to P x X'ΰ and Xlr x P\