论文标题
Sprays和Oka理论应用的隐式函数定理
An implicit function theorem for sprays and applications to Oka theory
论文作者
论文摘要
我们通过建立Spray的隐式函数定理来解决OKA理论中的基本问题。作为我们隐式函数定理的第一个应用，我们获得了一个基本证据，证明近似产生插值。该证明和拉鲁森的基本证明是匡威的基本证明，证明了近似和插值之间的等效性。第二个应用程序涉及爆炸的OKA属性。我们证明OKA沿平滑代数中心沿代数OKA歧管的爆炸。在附录中，等效的OKA歧管的特征是Gromov的条件$ \ Mathrm {ell} _ {1} $的等效版本，并且还给出了Equivariant本地化原则。
We solve fundamental problems in Oka theory by establishing an implicit function theorem for sprays. As the first application of our implicit function theorem, we obtain an elementary proof of the fact that approximation yields interpolation. This proof and Lárusson's elementary proof of the converse give an elementary proof of the equivalence between approximation and interpolation. The second application concerns the Oka property of a blowup. We prove that the blowup of an algebraically Oka manifold along a smooth algebraic center is Oka. In the appendix, equivariantly Oka manifolds are characterized by the equivariant version of Gromov's condition $\mathrm{Ell}_{1}$, and the equivariant localization principle is also given.
