Mathematical Research Letters

Volume 21 (2014)

Number 5

Oka properties of groups of holomorphic and algebraic automorphisms of complex affine space

Pages: 1047 – 1067

DOI: https://dx.doi.org/10.4310/MRL.2014.v21.n5.a7

Authors

Franc Forstnerič (Faculty of Mathematics and Physics, University of Ljubljana, and Institute of Mathematics, Physics, and Mechanics, Ljubljana, Slovenia)

Finnur Lárusson (School of Mathematical Sciences, University of Adelaide, Adelaide, South Australia)

Abstract

We show that the group of all holomorphic automorphisms of complex affine space $\mathbb{C}^n , n \gt 1$, and several of its subgroups satisfy the parametric Oka property with approximation and with interpolation on discrete sets.

Keywords

Stein manifold, Oka manifold, complex affine space, holomorphic automorphism, polynomial automorphism, approximation, interpolation

2010 Mathematics Subject Classification

Primary 32E10. Secondary 14R10, 32E30, 32H02, 32Q28.

Full Text (PDF format)

Accepted 18 July 2014

Published 9 December 2014