A remark on ultrahyperelliptic surfaces

Abstract

and every an is a simple zero of g(z) and s=0 or 1. Hiromi and Mutδ [1] proved the following result: Assume there exists a nontrivial analytic mapping φ from R into S. Then p=n-r, where r is the order of g(z) and n is an integer. The aim of the present paper is to prove the following THEOREM. If S is an ultrahyperelliptic surface of non-zero finite order into which there is a non-trivial analytic mapping from an ultrahyperelliptic surface R of finite order and with P(7?)=4, then the order of S is a half of an integer. 2. Proof of theorem. For our purpose we need our previous result in [4], which asserts the existence of two functions h(z) and f(z) such that f(z) is meromorphic in |2|

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关于超椭圆曲面的评述

每个an都是g(z)的一个简单的0 s=0或1。Hiromi和Mutδ[1]证明了以下结果:假设存在一个从R到s的非平凡解析映射φ，则p=n- R，其中R为g(z)的阶，n为整数。本文的目的是证明下列定理。如果S是一个非零有限阶超椭圆曲面，其中存在一个有限阶超椭圆曲面R的非平凡解析映射，且P(7?)=4，则S的阶为整数的二分之一。2. 定理的证明。为了我们的目的，我们需要之前在[4]中的结果，该结果断言了两个函数h(z)和f(z)的存在性，使得f(z)在|| < 0的情况下是亚纯的，并且h(z)是满足当前情况[1]的n次多项式

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