论文标题
尸体形态图的合理近似
Rational approximation of holomorphic maps
论文作者
论文摘要
令X为复杂的非源代数多样性，k的X圆形凸子集，y对于某些复杂的线性代数基团的均匀品种。我们证明，h-型图f：k-> y可以在k上通过常规映射k-> y在k上均匀近似，> y时，只有当f与常规地图k- k-> y是同型。但是，可能会发生一个无效的同型全体形态图K-> y不接受常规映射x在k上均匀的近似值 - > y。在这里，如果存在开放式（zariski open）k k中的k和h：h：u- h：u-> y，则为g：k-> y称为holomorphic（resp。常规），如果有一个开放式（zariski open）u的邻里u - u-> y。
Let X be a complex nonsingular affine algebraic variety, K a holomorphically convex subset of X, and Y a homogeneous variety for some complex linear algebraic group. We prove that a holomorphic map f:K-->Y can be uniformly approximated on K by regular maps K-->Y if and only if f is homotopic to a regular map K-->Y. However, it can happen that a null homotopic holomorphic map K-->Y does not admit uniform approximation on K by regular maps X-->Y. Here, a map g:K-->Y is called holomorphic (resp. regular) if there exist an open (resp. a Zariski open) neighborhood U of K in X and a holomorphic (resp. regular) map h:U-->Y such that h|K=g.
