Topology related to Valuation problems and Numerical Computations

考虑由从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E. K. Yamaguchi的所有临界点所构成的空间是非常重要的，他成功地定义了从亏格为g的Riemann曲面到复射影空间（g> 0）的有限维同伦位形空间模型。他还获得了类似的结果空间之间的代数映射真实的射影空间。此外，他表明，同伦渐近稳定性定理持有这种空间的代数映射。Kida研究椭圆曲线和与代数环面上某些映射相关的代数域扩展。作为一个应用，他获得了一个简单的方法检查素数。M.Ohno研究了非奇异投射簇上的向量丛，并从“nef值”的角度对其进行了研究。Yamada研究了4-流形的拓扑，并得到了一些与Gluck手术有关的结果。

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.