Studies on meromorphic convexity in Stein spaces
Studies on meromorphic convexity in Stein spaces
批准号:
18540188
负责人:
ABE Makoto
金额:
$1.39万
依托单位:
依托单位国家:
日本
项目类别:
Grant-in-Aid for Scientific Research (C)
财政年份:
2006
资助国家:
日本
项目状态:
已结题
起止时间:
2006 至 2007
中文摘要
与Stein空间中的亚纯凸性相联系,Makoto Abe得到了以下结果。(1)证明了C ^n中存在一个非多项式凸的开集D,当n ≥ 2时,该开集D满足强圆盘性质。这也对Bremermann(1958)的问题给出了否定的答案。(2)通过考虑可能非约Cohen-Macaulay Stein空间开集的局部Steinness,利用标准同态Div(D)→Pic(D)的满射性,证明了n维Stein流形X的开集D的Steinness满足dim H^k(D,O)< +∞(2 <$k <$n-1)的条件. (3)通过举例证明了C^n中的有理凸开集D(n ≠ 2)一般不满足C^n中的强亚纯逼近性质.证明了1维约化Stein空间X的每个开集D都满足X中的强亚纯逼近性质。(4)得到了约化Stein空间X中关于Picard群Pic(X)的子半群G的一个广义亚纯逼近定理,它包含了Hirschowitz(1971)和Abe(2005)的两个不同的亚纯逼近定理。(5)设G是一般线性群GL(2,C)的有限小子群.然后对C^2/G的极小正规解析紧化中的边界对偶图进行了分类,这是Abe-Furushima-Yamasaki(2000)和Abe-Furushima-Shima(2004)的工作的继续.
英文摘要
Connected to the meromorphic convexity in Stein spaces, Makoto Abe obtained the following results.(1) It is proved that there exists an open set D of C^n which is not polynomially convex and satisfies the strong disk property in C^n if n≧2. This also gives a negative answer to the problem of Bremermann(1958).(2) By considering the local Steinness for an open set of possibly non-reduced Cohen-Macaulay Stein space, it is proved that the Steinness of an open set D of a Stein manifold X of dimension n satisfying the condition that dim H^k(D, O)< +∞ (2≦k ≦n-1) by the surjectivity of the canonical homomorphism Div(D)→Pic(D).(3) By giving examples, it is proved that a rationally convex open set D of C^n, where n≧2, does not satisfy in general the strong meromorphic approximation property in C^n. It is also proved that every open set D of a reduced Stein space X of dimension 1 satisfies the strong meromorphic approximation property in X.(4) A generalized meromorphic approximation theorem in a reduced Stein space X with respect to a subsemigroup G of the Picard group Pic(X)is obtained, which includes both two different meromorphic approximation theorems due to Hirschowitz(1971) and due to Abe (2005).Tadashi Shima(with Mikio Furushima and Yasuhiro Ohshima) obtained the following result.(5) Let G be a small finite subgroup of general linear group GL(2, C). Then the classification of the dual graphs of the boundaries in the minimal normal analytic compactifications of C^2/G is completed, which is a continuation of the earlier works due to Abe-Furushima-Yamasaki (2000) and Abe-Furushima-Shima (2004).
期刊论文(0)
专著(0)
科研奖励(0)
会议论文
登录
查看更多内容
DOI:
--
发表时间:
2007
期刊:
影响因子:
--
作者:
[Makoto, Abe]
通讯作者:
Abe
DOI:
--
发表时间:
2006
期刊:
Toyama Math. J. 28(accepted)
影响因子:
--
作者:
[水谷祐介, 内田裕久, Baryshev Alexander, 井上光輝, Makoto Abe]
通讯作者:
Makoto Abe
Stein多様体の領域上の正則直線束と因子
斯坦因流形域上的正则线丛和因子
DOI:
--
发表时间:
2007
期刊:
影响因子:
--
作者:
[鍋島陽一, 今井真一郎, 名和田 新, 阿部 誠]
通讯作者:
阿部 誠
Meromorphic approximation theorems in a Stein space(in Japanese)
斯坦因空间中的亚纯逼近定理(日语)
DOI:
--
发表时间:
2007
期刊:
影响因子:
--
作者:
[Makoto, Abe]
通讯作者:
Abe
「研究成果報告書概要(和文)」より
摘自《研究结果报告摘要(日文)》
DOI:
--
发表时间:
2005
期刊:
影响因子:
--
作者:
[Kawauchi, et. al., Nishimura et al., Dezawa et al., Yoshizawa et al., 星野 幹雄, 星野 幹雄]
通讯作者:
星野 幹雄
共 9 条
Studies on intermediate pseudoconvexity in complex spaces
-
批准号:17K05301
-
项目类别:Grant-in-Aid for Scientific Research (C)
-
资助金额:$2.33万
-
财政年份:2017
-
负责人:ABE Makoto
-
依托单位:
Development of health monitoring system using clothing-type photoplethysmogram
-
批准号:25870040
-
项目类别:Grant-in-Aid for Young Scientists (B)
-
资助金额:$1.75万
-
财政年份:2013
-
负责人:ABE Makoto
-
依托单位:
Derivation of customer lifetime value and building decision support model for a company
-
批准号:25380562
-
项目类别:Grant-in-Aid for Scientific Research (C)
-
资助金额:$1.66万
-
财政年份:2013
-
负责人:ABE Makoto
-
依托单位:
Study on insect feeding resistance mechanism of bur gourd, Sicyos angulatus
-
批准号:23658052
-
项目类别:Grant-in-Aid for Challenging Exploratory Research
-
资助金额:$2.5万
-
财政年份:2011
-
负责人:ABE Makoto
-
依托单位:
Role of Trps1 in temporomandibular development
-
批准号:23592698
-
项目类别:Grant-in-Aid for Scientific Research (C)
-
资助金额:$3.33万
-
财政年份:2011
-
负责人:ABE Makoto
-
依托单位:
English Writing Activities Using Peer Learning: Noticing of the Language and the Role of Model Text
-
批准号:22520602
-
项目类别:Grant-in-Aid for Scientific Research (C)
-
资助金额:$1.75万
-
财政年份:2010
-
负责人:ABE Makoto
-
依托单位:
Role of retinoic acid catabolising enzyme in craniofacial development
-
批准号:21791785
-
项目类别:Grant-in-Aid for Young Scientists (B)
-
资助金额:$2.75万
-
财政年份:2009
-
负责人:ABE Makoto
-
依托单位:
DIVISORS AND MEROMORPHIC CONVEXITY IN A STEIN SPACE
-
批准号:20540180
-
项目类别:Grant-in-Aid for Scientific Research (C)
-
资助金额:$2.66万
-
财政年份:2008
-
负责人:ABE Makoto
-
依托单位:
Buying Behavior and Customer Lifetime Value in CRM
-
批准号:19530383
-
项目类别:Grant-in-Aid for Scientific Research (C)
-
资助金额:$1.66万
-
财政年份:2007
-
负责人:ABE Makoto
-
依托单位:
Role of Hand2 in osteoblast differentiation
-
批准号:19791344
-
项目类别:Grant-in-Aid for Young Scientists (B)
-
资助金额:$2.36万
-
财政年份:2007
-
负责人:ABE Makoto
-
依托单位:
Exploration on an Expansion of Production by Japanese Manufactures based in China and its Influence over Japanese Economy
-
批准号:17530218
-
项目类别:Grant-in-Aid for Scientific Research (C)
-
资助金额:$1.95万
-
财政年份:2005
-
负责人:ABE Makoto
-
依托单位:
Decision Support System for CRM based on an Individual Level Model
-
批准号:15530282
-
项目类别:Grant-in-Aid for Scientific Research (C)
-
资助金额:$1.02万
-
财政年份:2003
-
负责人:ABE Makoto
-
依托单位:
Global Production of Japanese Multinationals and its Consequences for Industries and Employment in Japan : case of electrical appliance industry
-
批准号:14530062
-
项目类别:Grant-in-Aid for Scientific Research (C)
-
资助金额:$1.22万
-
财政年份:2002
-
负责人:ABE Makoto
-
依托单位:
INVESTIGATING BEHAVIORAL EXPLANATIONS FOR ASYMMETRIC PRICE COMPETITION
-
批准号:11680439
-
项目类别:Grant-in-Aid for Scientific Research (C)
-
资助金额:$1.15万
-
财政年份:1999
-
负责人:ABE Makoto
-
依托单位:
Some Structural Changes of the Labor Market under the New Technology and the Industrial Relations
-
批准号:04630030
-
项目类别:Grant-in-Aid for General Scientific Research (C)
-
资助金额:$0.9万
-
财政年份:1992
-
负责人:ABE Makoto
-
依托单位:
海外基金