The Oka principle, lifting of holomorphic maps and removability of intersections

2001/01/29 by Franc Forstnerič, Franc Forstneric, Forstneric, Franc
Mathematics · #32H02 #32L05 #32Q28 #32Q55 #Advanced Algebra and Geometry #Complex Variables (math.CV) #FOS: Mathematics #Geometric and Algebraic Topology #Holomorphic and Operator Theory #math.CV #msc:32H02 #msc:32L05 #msc:32Q28 #msc:32Q55

paper · pdf · doi:10.48550/arxiv.math/0101238

Proc. of the Hayama Symposium on Several Complex Variables (Hayama 2000), pp. 49--59, Japan, 2001

openalex publication_date 2001/01/29 · arxiv created 2003/05/16 · arxiv updated 2009/11/30 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

The paper is related to the author's talk at the Hayama Symposium in Complex Analysis in December 2000. In section 1 we survey results on the Oka principle for sections of holomorphic submersions over Stein manifolds. In section 2 we apply these results to the lifting problem for holomorphic mappings from Stein manifolds, and in section 3 we apply them to the problem of removability of intersections of holomorphic maps from Stein manifolds with closed complex subvarieties of the target space.

Related

• The homotopy principle in complex analysis: a survey
• The Oka principle for sections of subelliptic submersions
• Oka's principle for holomorphic submersions with sprays
• Recent developments on Oka manifolds
• Absolute neighbourhood retracts and spaces of holomorphic maps from Stein manifolds to Oka manifolds