On the embedding and compactification of q -complete manifolds

Ionuţ Chiose[1]

  • [1] University of Illinois at Chicago Department of Mathematics, Statistics, and Computer Science 851 South Morgan Street Chicago, Illinois 60607 (USA) & Romanian Academy Institute of Mathematics RO-70700 Bucharest (Romania)

Annales de l’institut Fourier (2006)

  • Volume: 56, Issue: 2, page 373-396
  • ISSN: 0373-0956

Abstract

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We characterize intrinsically two classes of manifolds that can be properly embedded into spaces of the form ℙ N ∖ ℙ N - q . The first theorem is a compactification theorem for pseudoconcave manifolds that can be realized as X ¯ ∖ ( X ¯ ∩ ℙ N - q ) where X ¯ ⊂ ℙ N is a projective variety. The second theorem is an embedding theorem for holomorphically convex manifolds into ℙ 1 × ℂ N .

How to cite

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Chiose, Ionuţ. "On the embedding and compactification of $q$-complete manifolds." Annales de l’institut Fourier 56.2 (2006): 373-396. <http://eudml.org/doc/10150>.

@article{Chiose2006,
abstract = {We characterize intrinsically two classes of manifolds that can be properly embedded into spaces of the form $\mathbb\{ P\}^N\setminus \mathbb\{ P\}^\{N-q\}$. The first theorem is a compactification theorem for pseudoconcave manifolds that can be realized as $\overline\{X\}\setminus (\overline\{X\}\cap \mathbb\{ P\}^\{N-q\})$ where $\overline\{X\}\subset \mathbb\{ P\}^N$ is a projective variety. The second theorem is an embedding theorem for holomorphically convex manifolds into $\mathbb\{ P\}^1\times \mathbb\{ C\}^N$.},
affiliation = {University of Illinois at Chicago Department of Mathematics, Statistics, and Computer Science 851 South Morgan Street Chicago, Illinois 60607 (USA) & Romanian Academy Institute of Mathematics RO-70700 Bucharest (Romania)},
author = {Chiose, Ionuţ},
journal = {Annales de l’institut Fourier},
keywords = {Pseudoconvex and pseudoconcave spaces; embeddings and compactifications; positive line bundles; Remmert reduction; pseudoconvex space; pseudoconcave space; embedding; compactification},
language = {eng},
number = {2},
pages = {373-396},
publisher = {Association des Annales de l’institut Fourier},
title = {On the embedding and compactification of $q$-complete manifolds},
url = {http://eudml.org/doc/10150},
volume = {56},
year = {2006},
}

TY - JOUR
AU - Chiose, Ionuţ
TI - On the embedding and compactification of $q$-complete manifolds
JO - Annales de l’institut Fourier
PY - 2006
PB - Association des Annales de l’institut Fourier
VL - 56
IS - 2
SP - 373
EP - 396
AB - We characterize intrinsically two classes of manifolds that can be properly embedded into spaces of the form $\mathbb{ P}^N\setminus \mathbb{ P}^{N-q}$. The first theorem is a compactification theorem for pseudoconcave manifolds that can be realized as $\overline{X}\setminus (\overline{X}\cap \mathbb{ P}^{N-q})$ where $\overline{X}\subset \mathbb{ P}^N$ is a projective variety. The second theorem is an embedding theorem for holomorphically convex manifolds into $\mathbb{ P}^1\times \mathbb{ C}^N$.
LA - eng
KW - Pseudoconvex and pseudoconcave spaces; embeddings and compactifications; positive line bundles; Remmert reduction; pseudoconvex space; pseudoconcave space; embedding; compactification
UR - http://eudml.org/doc/10150
ER -

References

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  8. L. Hörmander, An introduction to complex analysis in several variables, (1966), D. Van Nostrand Co., Inc., Princeton, N.J.-Toronto, Ont.-London Zbl0138.06203
  9. N. Mok, An embedding theorem of complete Kähler manifolds of positive bisectional curvature onto affine algebraic varieties, Bull. Soc. Math. France 112 (1984), 197-250 Zbl0536.53062
  10. A. Nadel, On complex manifolds which can be compactified by adding finitely many points, Invent. Math. 101 (1990), 173-189 Zbl0712.32019
  11. T. Ohsawa, Hodge spectral sequence and symmetry on compact Kähler spaces, Publ. Res. Inst. Math. Sci. 23 (1987), 613-625 Zbl0635.32008
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