# THE OKA PRINCIPLE FOR SECTIONS OF SUBELLIPTIC SUBMERSIONS

Mathematische Zeitschrift（2002）

摘要

Let X and Y be complex manifolds. One says that maps from X to Y satisfy the
Oka principle if the inclusion of the space of holomorphic maps from X to Y
into the space of continuous maps is a weak homotopy equivalence. In 1957 H.
Grauert proved the Oka principle for maps from Stein manifolds to complex Lie
groups and homogeneous spaces, as well as for sections of fiber bundles with
homogeneous fibers over a Stein base. In 1989 M. Gromov extended Grauert's
result to sections of submersions over a Stein base which admit dominating
sprays over small open sets in the base; for proof see [F. Forstneric and J.
Prezelj: Oka's principle for holomorphic fiber bundles with sprays, Math. Ann.
317 (2000), 117-154, and the preprint math.CV/0101040].
In this paper we prove the Oka principle for maps from Stein manifolds to any
complex manifold Y that admits finitely many sprays which together dominate at
every point of Y (such manifold is called subelliptic). The class of
subelliptic manifolds contains all the elliptic ones, as well as complements of
closed algebraic subvarieties of codimension at least two in a complex
projective space or a complex Grassmanian. We also prove the Oka principle for
removing intersections of holomorphic maps with closed complex subvarieties A
of the target manifold Y, provided that the source manifold is Stein and the
manifolds Y and Y\A are subelliptic.

更多查看译文

关键词

satisfiability,homogeneous space,complex projective space,complex manifold,lie group,stein manifold

AI 理解论文

溯源树

样例

生成溯源树，研究论文发展脉络