抄録
Offer Organization: Japan Society for the Promotion of Science, System Name: Grants-in-Aid for Scientific Research, Category: Grant-in-Aid for Scientific Research (C), Fund Type: -, Overall Grant Amount: - (direct: 3400000, indirect: -)
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.