scholarly journals Holomorphic maps from rational homogeneous spaces onto projective manifolds

2009 ◽  
Vol 18 (2) ◽  
pp. 223-256 ◽  
Author(s):  
Chi-Hin Lau
Keyword(s):  
Homogeneous Spaces ◽  
Holomorphic Maps ◽  
Projective Manifolds

scholarly journals Approximation and interpolation of regular maps from affine varieties to algebraic manifolds

2019 ◽  
Vol 125 (2) ◽  
pp. 199-209 ◽  
Author(s):  
Finnur Lárusson ◽  
Tuyen Trung Truong
Keyword(s):  
Toric Varieties ◽  
The Other ◽  
Rational Curve ◽  
Complex Manifolds ◽  
Holomorphic Maps ◽  
New Class ◽  
Regular Maps ◽  
Projective Manifolds ◽  
Definition Of ◽  
Algebraic Manifolds

We consider the analogue for regular maps from affine varieties to suitable algebraic manifolds of Oka theory for holomorphic maps from Stein spaces to suitable complex manifolds. The goal is to understand when the obstructions to approximation or interpolation are purely topological. We propose a definition of an algebraic Oka property, which is stronger than the analytic Oka property. We review the known examples of algebraic manifolds satisfying the algebraic Oka property and add a new class of examples: smooth nondegenerate toric varieties. On the other hand, we show that the algebraic analogues of three of the central properties of analytic Oka theory fail for all compact manifolds and manifolds with a rational curve; in particular, for projective manifolds.

scholarly journals Interpolation by holomorphic maps from the disc to the tetrablock

2021 ◽  
Vol 498 (2) ◽  
pp. 124951
Author(s):  
Hadi O. Alshammari ◽  
Zinaida A. Lykova
Keyword(s):  
Holomorphic Maps
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