Topology related to Valuation problems and Numerical Computations

与估值问题和数值计算相关的拓扑

• 批准号: 13640067
• 负责人: YAMAGUCHI Kohei
• 金额: $ 2.18万
• 依托单位: The University of Electro-Communications
• 依托单位国家: 日本
• 项目类别: Grant-in-Aid for Scientific Research (C)
• 财政年份: 2001
• 资助国家: 日本
• 起止时间: 2001 至 2003
• 项目状态: 已结题
• 来源: https://kaken.nii.ac.jp/grant/KAKENHI-PROJECT-13640067/
• 关键词: projective variety; Riemann surface; energy functional; configuration space; harmonic map; elliptic curve; algebraic torus; asymptic stability; リーマン画; ラベル付き粒子の配置空間; ラグラジアン; ホモトピー型; 正則写像; 曲面結び目; labelled configuration space; 射影空間; モース理論的原理

Consider the energy functionals E on spaces consisting of all smooth maps from a Riemann surface to complex projective spaces. In this case, it is very important to study the spaces consisting of all critical points of E.K.Yamaguchi suceeds to define a finite dimensional homotopy configuration space models from a Riemann surface of genus g into a complex projective space for g>O. He also obtains a similar result for the space of algebraic maps between real projective spaces. Moreover, he shows that a homotopy asymptic stability theorem holds for such spaces of algebraic maps. Kida studies elliptic curves and algebraic field extensions associated to certain maps on algebraic torus. As an application he obtains an easy method for checking prime numbers. M.Ohno studied the vector bundles over non-singular projective varieties and investigated them from the point of view of "nef value". Y.Yamada studied the topology of 4-manifolds and obtained several results related to Gluck surgery.

考虑由黎曼曲面到复射影空间的所有光滑映射组成的空间上的能量泛函E。在这种情况下，研究由所有临界点组成的空间是非常重要的。E.K.Yamaguchi成功地定义了从g属的Riemann曲面到g b> O的复射影空间的有限维同伦组态空间模型。对于实射影空间之间的代数映射空间，他也得到了类似的结果。此外，他还证明了这种代数映射空间的一个同伦渐近稳定性定理。Kida研究了与代数环面上某些映射相关的椭圆曲线和代数域扩展。作为一种应用，他得到了一种检验素数的简便方法。m.o ohno研究了非奇异投影簇上的向量束，并从“nef值”的角度进行了研究。Y.Yamada研究了4流形的拓扑结构，并获得了一些与Gluck手术相关的结果。

项目成果

K.Yamaguchi: "Mod p truncated configuration spaces"J.Math.Soc.Japan. 56-1. 193-199 (2004)

K.Yamaguchi：“Mod p 截断配置空间”J.Math.Soc.Japan。

K.Yamaguchi: "Configuration space models for spaces of maps from a Riemann surface to complex projective space"Publ.Res.Inst.Math.Soc.. 39-3. 535-543 (2003)

K.Yamaguchi：“从黎曼曲面到复射影空间的映射空间的配置空间模型”Publ.Res.Inst.Math.Soc.. 39-3。

K.Yamaguchi: "Universal coverings of spaces of holomorphic maps"Kyushu J. Math.. 56-2. 381-389 (2002)

K.Yamaguchi：“全纯映射空间的通用覆盖”Kyushu J. Math.. 56-2。

Kohhei Yamaguchi: "Spaces of holomorphic maps with bounded multiplicity"Quart. J. Math.. 52. 249-259 (2001)

Kohhei Yamaguchi：“具有有限多重性的全纯映射空间”夸脱。

A.Kozlowski, K.Yamaguchi: "Spaces of holomorphic maps between complex projective spaces of degree one"Topology and Its Applications. 132-2. 139-145 (2003)

A.Kozlowski、K.Yamaguchi：“一级复射影空间之间的全纯映射空间”拓扑及其应用。