scholarly journals Extending Nirenberg–Spencer’s question on holomorphic embeddings to families of holomorphic embeddings

2021 ◽  
Vol 170 (15) ◽  
Author(s):  
Jun-Muk Hwang
Keyword(s):  
Holomorphic Embeddings

scholarly journals Holomorphic embeddings of planar domains intoC 2

1995 ◽  
Vol 303 (1) ◽  
pp. 579-597 ◽  
Author(s):  
Josip Globevnik ◽  
Berit Stens�nes
Keyword(s):  
Planar Domains ◽  
Holomorphic Embeddings

scholarly journals A construction of complete complex hypersurfaces in the ball with control on the topology

2019 ◽  
Vol 2019 (751) ◽  
pp. 289-308 ◽  
Author(s):  
Antonio Alarcón ◽  
Josip Globevnik ◽  
Francisco J. López
Keyword(s):  
Unit Ball ◽  
Compact Subset ◽  
Unit Disc ◽  
Finite Topology ◽  
Complex Curves ◽  
Holomorphic Embedding ◽  
Holomorphic Embeddings

AbstractGiven a closed complex hypersurface {Z\subset\mathbb{C}^{N+1}} ({N\in\mathbb{N}}) and a compact subset {K\subset Z}, we prove the existence of a pseudoconvex Runge domain D in Z such that {K\subset D} and there is a complete proper holomorphic embedding from D into the unit ball of {\mathbb{C}^{N+1}}. For {N=1}, we derive the existence of complete properly embedded complex curves in the unit ball of {\mathbb{C}^{2}}, with arbitrarily prescribed finite topology. In particular, there exist complete proper holomorphic embeddings of the unit disc {\mathbb{D}\subset\mathbb{C}} into the unit ball of {\mathbb{C}^{2}}. These are the first known examples of complete bounded embedded complex hypersurfaces in {\mathbb{C}^{N+1}} with any control on the topology.

scholarly journals An interpolation theorem for proper holomorphic embeddings

2007 ◽  
Vol 338 (3) ◽  
pp. 545-554 ◽  
Author(s):  
Franc Forstnerič ◽  
Björn Ivarsson ◽  
Frank Kutzschebauch ◽  
Jasna Prezelj
Keyword(s):  
Interpolation Theorem ◽  
Holomorphic Embeddings

scholarly journals A Carleman type theorem for proper holomorphic embeddings

1997 ◽  
Vol 35 (1) ◽  
pp. 157-169 ◽  
Author(s):  
Gregery T. Buzzard ◽  
Franc Forstneric
Keyword(s):  
Type Theorem ◽  
Carleman Type ◽  
Holomorphic Embeddings

scholarly journals Projective Bundles on Infinite-Dimensional Complex Spaces

2004 ◽  
Vol 11 (1) ◽  
pp. 43-48
Author(s):  
E. Ballico
Keyword(s):  
Banach Space ◽  
Vector Bundle ◽  
Holomorphic Vector Bundle ◽  
Line Bundles ◽  
Holomorphic Line Bundle ◽  
Infinite Dimensional ◽  
Complex Spaces ◽  
Projective Bundles ◽  
Holomorphic Embeddings ◽  
Holomorphic Line Bundles

Abstract Let V be a complex localizing Banach space with countable unconditional basis and E a rank r holomorphic vector bundle on P(V). Here we study the holomorphic embeddings of P(E) into products of projective spaces and the holomorphic line bundles on P(E). In particular we prove that if r ≥ 3, then H 1(P(E), L) = 0 for every holomorphic line bundle L on P(E).

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