Algebraic vaieties with Kodaira dimansion O and A generalization of the Bogomolor-decomposition
具有 Kodaira 维 O 的代数簇和 Bogomolor 分解的 A 推广
基本信息
- 批准号:12440007
- 负责人:
- 金额:$ 3.46万
- 依托单位:
- 依托单位国家:日本
- 项目类别:Grant-in-Aid for Scientific Research (B)
- 财政年份:2000
- 资助国家:日本
- 起止时间:2000 至 2002
- 项目状态:已结题
- 来源:
- 关键词:
项目摘要
Does the period of the second cohomology determine an isomorphism class of a complex irreducible symplectic manifold? This is the Torelli problem. It is true for a K3 surface, but there is an counter-example of Debarre for dim 【greater than or equal】 4. Mukai, Huybrechts and others have posed the birational Torelli problem modifying the original one. We construeted a counter-example even for this problem.On the other hand, for a complex irreducible symplectic manifold, which kind of information on the original variety can be recoverd from the derived category of coherent sheaves ? When do we have an equivalence of derived categories of two complex irreducible manifolds ? Such questions are quite interesting. We proved that the derived categories are equivalent if two smooth projective varieties are connected by a Mukai flop. As an application, one knows that birationally equivalent, complex, projective symplectic 4-folds have equivalent derived categories.We also studied the deformation theory of complex symplectic varieties and generalized several important facts on a complex symplectic manifold to a singular symplectic variety.
复不可约辛流形的二阶上同调的周期决定同构类吗?这就是Torelli的问题。这对于K3曲面是正确的,但对于dim [大于或等于] 4,存在Debarre的反例。Mukai,Huybrechts和其他人提出了修改原始问题的双理性Torelli问题。另一方面,对于复的不可约辛流形,从凝聚层的导出范畴中可以得到关于原簇的哪类信息?什么时候两个复不可约流形的导范畴是等价的?这类问题很有意思。我们证明了如果两个光滑投射簇由一个Mukai翻转连接,则导出范畴是等价的。作为应用,我们知道双有理等价的复射影辛4-folds有等价的导范畴,我们还研究了复辛簇的变形理论,并将复辛流形上的几个重要事实推广到奇异辛簇上。
项目成果
期刊论文数量(66)
专著数量(0)
科研奖励数量(0)
会议论文数量(0)
专利数量(0)
宮西正宜(共著): "Open algebraic surfaces with finite group actions"Transform.Groups. 7. 185-207 (2002)
Masanori Miyanishi(合著者):“具有有限群作用的开放代数曲面”Transform.Groups。 7. 185-207 (2002)
- DOI:
- 发表时间:
- 期刊:
- 影响因子:0
- 作者:
- 通讯作者:
並河良典: "Calabi-Yaus and Deformation Theory"Sugaku exposition, American Math.Soc.. (刊行予定). (2001)
Yoshinori Namikawa:“Calabi-Yaus 和变形理论”Sugaku 阐述,American Math.Soc.(即将出版)(2001 年)。
- DOI:
- 发表时间:
- 期刊:
- 影响因子:0
- 作者:
- 通讯作者:
藤木明: "Compact self-dual manifolds with torus actions"J.Diff Geometry. (刊行予定).
Akira Fujiki:“具有环面作用的紧凑自对偶流形”J.Diff Geometry(即将出版)。
- DOI:
- 发表时间:
- 期刊:
- 影响因子:0
- 作者:
- 通讯作者:
"Stratified local moduli of Calabi-Yau threefolds"Topology. 41. 1219-1237 (2002)
“卡拉比-丘三重分层局部模”拓扑。
- DOI:
- 发表时间:
- 期刊:
- 影响因子:0
- 作者:
- 通讯作者:
藤木明: "Topology of compact self-dual manifolds whose twbfor space is of positive algebraic dimension"J.Math.Soc.Japan. 54. 587-608 (2002)
Akira Fujiki:“twb 空间具有正代数维数的紧致自对偶流形的拓扑”J.Math.Soc.Japan 54. 587-608 (2002)。
- DOI:
- 发表时间:
- 期刊:
- 影响因子:0
- 作者:
- 通讯作者:
{{
item.title }}
{{ item.translation_title }}
- DOI:
{{ item.doi }} - 发表时间:
{{ item.publish_year }} - 期刊:
- 影响因子:{{ item.factor }}
- 作者:
{{ item.authors }} - 通讯作者:
{{ item.author }}
数据更新时间:{{ journalArticles.updateTime }}
{{ item.title }}
- 作者:
{{ item.author }}
数据更新时间:{{ monograph.updateTime }}
{{ item.title }}
- 作者:
{{ item.author }}
数据更新时间:{{ sciAawards.updateTime }}
{{ item.title }}
- 作者:
{{ item.author }}
数据更新时间:{{ conferencePapers.updateTime }}
{{ item.title }}
- 作者:
{{ item.author }}
数据更新时间:{{ patent.updateTime }}
NAMIKAWA Yoshinori其他文献
NAMIKAWA Yoshinori的其他文献
{{
item.title }}
{{ item.translation_title }}
- DOI:
{{ item.doi }} - 发表时间:
{{ item.publish_year }} - 期刊:
- 影响因子:{{ item.factor }}
- 作者:
{{ item.authors }} - 通讯作者:
{{ item.author }}
{{ truncateString('NAMIKAWA Yoshinori', 18)}}的其他基金
The geometry of complex symplectic varieties
复辛簇的几何
- 批准号:
21340005 - 财政年份:2009
- 资助金额:
$ 3.46万 - 项目类别:
Grant-in-Aid for Scientific Research (B)
Complex symplectic varieties
复辛簇
- 批准号:
18340009 - 财政年份:2006
- 资助金额:
$ 3.46万 - 项目类别:
Grant-in-Aid for Scientific Research (B)
Complex symplectic varieties and derived categories
复辛簇和派生范畴
- 批准号:
15340008 - 财政年份:2003
- 资助金额:
$ 3.46万 - 项目类别:
Grant-in-Aid for Scientific Research (B)
相似海外基金
DERIVED CATEGORY METHODS IN ARITHMETIC: AN APPROACH TO SZPIRO'S CONJECTURE VIA HOMOLOGICAL MIRROR SYMMETRY AND BRIDGELAND STABILITY CONDITIONS
算术中的派生范畴方法:通过同调镜像对称性和布里奇兰稳定性条件推导SZPIRO猜想
- 批准号:
EP/V047299/1 - 财政年份:2021
- 资助金额:
$ 3.46万 - 项目类别:
Research Grant
McKay correspondence and derived category
麦凯对应及派生类别
- 批准号:
19K03444 - 财政年份:2019
- 资助金额:
$ 3.46万 - 项目类别:
Grant-in-Aid for Scientific Research (C)
Generalized complex structures, 4 dimensional differential topology, noncommutative algebraic geometry and derived category
广义复结构、4维微分拓扑、非交换代数几何和派生范畴
- 批准号:
16K13755 - 财政年份:2016
- 资助金额:
$ 3.46万 - 项目类别:
Grant-in-Aid for Challenging Exploratory Research
integrable system and moduli theory of derived category
可积系统与派生范畴模论
- 批准号:
26400043 - 财政年份:2014
- 资助金额:
$ 3.46万 - 项目类别:
Grant-in-Aid for Scientific Research (C)
Research on generalized geometric structures, 4 dimensional differential topology and derived category
广义几何结构、4维微分拓扑及派生范畴研究
- 批准号:
25610011 - 财政年份:2013
- 资助金额:
$ 3.46万 - 项目类别:
Grant-in-Aid for Challenging Exploratory Research
Study of problems related to derived category of coherent sheaves
相干滑轮派生范畴相关问题的研究
- 批准号:
25800017 - 财政年份:2013
- 资助金额:
$ 3.46万 - 项目类别:
Grant-in-Aid for Young Scientists (B)
Moduli of vector bundles with connection and derived category
具有连接和派生范畴的向量丛的模
- 批准号:
22740014 - 财政年份:2010
- 资助金额:
$ 3.46万 - 项目类别:
Grant-in-Aid for Young Scientists (B)