Analytic Sets and Complex Spaces

2016 ◽  
pp. 203-279
Author(s):  
Junjiro Noguchi
Keyword(s):  
Complex Spaces ◽  
Analytic Sets

scholarly journals Real analytic sets in complex spaces and CR maps

2007 ◽  
Vol 256 (4) ◽  
pp. 757-767 ◽  
Author(s):  
Rasul Shafikov
Keyword(s):  
Complex Spaces ◽  
Analytic Sets ◽  
Real Analytic

Branched Coverings and Minimal Free Resolution for Infinite-Dimensional Complex Spaces

2003 ◽  
Vol 10 (1) ◽  
pp. 37-43
Author(s):  
E. Ballico
Keyword(s):  
Projective Space ◽  
Projective Spaces ◽  
Free Resolution ◽  
Complete Intersections ◽  
Vanishing Theorem ◽  
Sheaf Cohomology ◽  
Minimal Free Resolution ◽  
Branched Coverings ◽  
Infinite Dimensional ◽  
Complex Spaces

Abstract We consider the vanishing problem for higher cohomology groups on certain infinite-dimensional complex spaces: good branched coverings of suitable projective spaces and subvarieties with a finite free resolution in a projective space P(V ) (e.g. complete intersections or cones over finitedimensional projective spaces). In the former case we obtain the vanishing result for H 1. In the latter case the corresponding results are only conditional for sheaf cohomology because we do not have the corresponding vanishing theorem for P(V ).

ON DEFORMATIONS OF NON-COMPACT COMPLEX SPACES

1978 ◽  
Vol 33 (5) ◽  
pp. 181-182
Author(s):  
I F Donin
Keyword(s):  
Complex Spaces

scholarly journals Note on meromorphic mappings in complex spaces

1961 ◽  
Vol 13 (4) ◽  
pp. 410-415
Author(s):  
Kenkiti KASAHARA
Keyword(s):  
Complex Spaces ◽  
Meromorphic Mappings

scholarly journals Reflexive differential forms on singular spaces. Geometry and cohomology

2014 ◽  
Vol 2014 (697) ◽  
Author(s):  
Daniel Greb ◽  
Stefan Kebekus ◽  
Thomas Peternell
Keyword(s):  
Differential Forms ◽  
Extension Theorem ◽  
Singular Variety ◽  
Singular Spaces ◽  
Complex Spaces ◽  
Rationally Connected ◽  
Smooth Locus ◽  
Recent Extension ◽  
Rationally Connected Varieties

AbstractBased on a recent extension theorem for reflexive differential forms, that is, regular differential forms defined on the smooth locus of a possibly singular variety, we study the geometry and cohomology of sheaves of reflexive differentials.First, we generalise the extension theorem to holomorphic forms on locally algebraic complex spaces. We investigate the (non-)existence of reflexive pluri-differentials on singular rationally connected varieties, using a semistability analysis with respect to movable curve classes. The necessary foundational material concerning this stability notion is developed in an appendix to the paper. Moreover, we prove that Kodaira–Akizuki–Nakano vanishing for sheaves of reflexive differentials holds in certain extreme cases, and that it fails in general. Finally, topological and Hodge-theoretic properties of reflexive differentials are explored.

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