权益分类	功能权益	普通用户	{{item.name}}会员
{{category.name}}	{{benefitItem.name}}

The uniqueness and the degeneracy problems of meromorphic maps and the construction of meromorphic maps with deficient devisors.

亚纯映射的唯一性和简并性问题以及缺陷引数的亚纯映射的构造。

基本信息

批准号：
14540196
负责人：
ATSUJI Atsushi
金额：
$ 2.24万
依托单位：
Keio University (2004)Numazu National College of Technology (2002-2003)
依托单位国家：
日本
项目类别：
Grant-in-Aid for Scientific Research (C)
财政年份：
2002
资助国家：
日本
起止时间：
2002 至 2004
项目状态：
已结题

项目摘要

Our project was concerned with the value distribution of meromorphic maps,in particular, uniqueness problem, degeneration and the construction of meromorphic maps with their defect to arbitrary divisors. From 2002-2003 the project leader Aihara and Mori studied the construction of meromorphic maps with positive defect on given hypersurfaces. In particular, we showed that for an arbitrary effective divisor on complex projective spaces there exists an interval of real numbers such that we can always construct the meromorphic maps whose defect equals to each value in the interval. These researches enabled us to improve the estimate on the defect more sharply. We also determined the divisors which defects cannot be evaluated. Aihara also considered some uniqueness problem of meromorphic maps between analytic covering spaces of complex Euclidean spaces and complex projective spaces. He specially discussed which kinds of constraints to the uniqueness are caused by some geometric conditions. From these works we achieved the first aim of our project. We pushed our project forward to some related problems. In 2004, the generalization of the domain of meromorphic maps was considered mainly by the project leader Atsuji. We showed that Nevanlinna theory, the main tool of the theory of value distribution of meromorphic maps, can be established for meromorphic functions on general complete Kaehler manifolds.We also obtained the following results from 2002-2004 by the effort of the other members.Kitagawa considered a conjecture : the volume of the domain surrounded by a closed surface in 3-sphere is invariant under any isometric deformations of the closed surface. He obtained the affirmative answer to the conjecture in the case when the closed surface is a flat torus.Kamada showed that Hirzebruch surfaces which admit Kaehler metrics (may be indefinite) of constant scalar curvature, must be biholomorphic to a direct product of projective lines.

我们的项目主要研究了亚纯映射的值分布，特别是唯一性问题，退化问题，以及对任意因子有缺陷的亚纯映射的构造问题。从2002年到2003年，项目负责人Aihara和Mori研究了给定超曲面上具有正亏损的亚纯映射的构造。特别地，我们证明了对于复射影空间上的任意有效因子，存在一个真实的数区间，使得我们总能构造出亏度等于区间内每个值的亚纯映射.这些研究使我们能够更大幅度地提高对缺陷的估计。我们还确定了无法评估缺陷的因子。Aihara还考虑了复欧氏空间的解析覆盖空间与复射影空间之间的亚纯映射的唯一性问题。他特别讨论了几何条件对唯一性的限制。通过这些工作，我们实现了项目的第一个目标。我们把我们的项目推进到一些相关的问题上。2004年，亚纯映射域的推广主要由项目负责人Atsuji考虑。我们证明了亚纯映射值分布理论的主要工具Nevanlinna理论可以建立在一般完备Kaehler流形上的亚纯函数上。在2002-2004年期间，我们通过其他成员的努力得到了以下结果。Kitagawa考虑了一个猜想：三维球面中闭曲面所包围区域的体积在闭曲面的任何等距变形下都是不变的。他得到了肯定的答案猜想的情况下，当封闭的表面是一个平坦的torus.Kamada表明，Hirzebruch表面承认Kaehler度量（可能是不定的）的常数标量曲率，必须biholomorphic的直接产品的投影线。