Formal cohomology, analytic cohomology and non-algebraic manifolds

Siegmund Kosarew; Thomas Peternell

Compositio Mathematica (1990)

  • Volume: 74, Issue: 3, page 299-325
  • ISSN: 0010-437X

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Kosarew, Siegmund, and Peternell, Thomas. "Formal cohomology, analytic cohomology and non-algebraic manifolds." Compositio Mathematica 74.3 (1990): 299-325. <http://eudml.org/doc/90023>.

@article{Kosarew1990,
author = {Kosarew, Siegmund, Peternell, Thomas},
journal = {Compositio Mathematica},
keywords = {surfaces; analytic cohomology; formal cohomology; smooth compactification; irreducible divisor; projective manifold; existence of meromorphic functions},
language = {eng},
number = {3},
pages = {299-325},
publisher = {Kluwer Academic Publishers},
title = {Formal cohomology, analytic cohomology and non-algebraic manifolds},
url = {http://eudml.org/doc/90023},
volume = {74},
year = {1990},
}

TY - JOUR
AU - Kosarew, Siegmund
AU - Peternell, Thomas
TI - Formal cohomology, analytic cohomology and non-algebraic manifolds
JO - Compositio Mathematica
PY - 1990
PB - Kluwer Academic Publishers
VL - 74
IS - 3
SP - 299
EP - 325
LA - eng
KW - surfaces; analytic cohomology; formal cohomology; smooth compactification; irreducible divisor; projective manifold; existence of meromorphic functions
UR - http://eudml.org/doc/90023
ER -

References

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  1. [A] Arnold, V.I., Bifurcations of invariant manifolds of differential equations and normal forms in neighborhoods of elliptic curves. English transl. Funct. Anal. Appl.10 (1977) 249-257. Zbl0346.58003
  2. [A-G] Andreotti, A. and Grauert, H., Théorèmes de finitude pour la cohomologie des espaces complexes. Bull. Soc. math. France90 (1962) 193-259. Zbl0106.05501MR150342
  3. [B-K] Bingener, J. and Kosarew, S., Lokale Modulräume in der analytischen Geometrie. Vieweg Verlag, Braunschweig1987. Zbl0644.32001
  4. [Ba] Baran, A., Duality for the hyperext on complex spaces. Rev. Roum.31 (1986) 95-120. Zbl0604.32012MR839814
  5. [Bn] Bănică, C. and Stănăsilă, O., Algebraic Methods in the Global Theory of Complex Spaces. Ed. Academiei Bucuresti, John Wiley & Sons, London-New York-Sydney- Toronto1976. Zbl0334.32001MR463470
  6. [Bo] Borel, A. et al., Intersection cohomology. Progress in Math.50, Birkhäuser1984. Zbl0553.14002
  7. [BPV] Barth, W., Peters, C., Van de Ven, A., Compact complex surfaces. Erg. der Math. Vol. 4Bonn -Heidelberg-New York, Springer1984. Zbl0718.14023MR749574
  8. [E] Enoki, I., Surfaces of class VII with curves. Tôhoku Math. J.33 (1981) 453-492. Zbl0476.14013MR643229
  9. [F] Fritzsche, K., q-konvexe Restmengen in kompakten komplexen Mannigfaltigkeiten. Math. Ann.221 (1976) 251-273. Zbl0327.32007MR419840
  10. [Ha 1] Hartshorne, R., Residues and Duality. Springer LN in Math. 20, Berling-Heidelbeg-New York, 1966. Zbl0212.26101MR222093
  11. [Ha 2] Hartshorne, R., Ample Subvarieties of Algebraic Varieties. Springer LN in Math. 156, Berlin-Heidelberg- New York, 1970. Zbl0208.48901MR282977
  12. [Ha 3] Hartshorne, R., Algebraic Geometry. Graduate Texts in Math. Springer1977. Zbl0367.14001MR463157
  13. [I-P 1] Iljashenko, Y. and Pyartli, A., Neighborhoods of zero type in embedded complex tori. In: Topics in Modern Mathematics. Transl. from Petrovskii Sem. No. 5 (ed. O.A. Oleinik), New York1985. Zbl0664.32016
  14. [I-P 2] Iljashenko, Y. and Pyartli, A., Materialization of Poincaré resonances and divergence of normalizing series. Transl. from Petrovskii Sem. No. 7: J. Sov. Math.31 (1985) 3053-3092. Zbl0575.34037
  15. [K 1] Kodaira, K., On the structure of compact complex analytic surfaces II. Amer, J. Math.88 (1966) 682-721. Zbl0193.37701MR205280
  16. [K 2] Kodaira, K., On the structure of compact complex analytic surfaces IIIAmer. J. Math.90. (1969) 55-83. Zbl0193.37701MR228019
  17. [K 3] Kodaira, K., Holomorphic mappings of polydiscs into compact complex manifolds. J. Diff. Geo.6 (1971) 33-46. Zbl0227.32008MR301228
  18. [Ka] Karras, U., Local Cohomology along Exceptional sets. Math. Ann.275 (1986) 673-682. Zbl0583.32026MR859337
  19. [Ko 1] Kosarew, S., Ein Verschwindungssatz für gewisse Kohomologiegruppen in Umgebung kompakter komplexer Unterräume mit konvex/konkavem NormalenbündelMath. Ann.261 (1982) 315-326. Zbl0497.32014MR679793
  20. [Ko 2] Kosarew, S., Konvergenz formaler komplexer Räume mit konvexem oder konkavem Normalenbündel. J. reine angew. Math.340 (1983) 6-25. Zbl0534.32002MR691958
  21. [Ko 3] Kosarew, S., Modulräume holomorpher Abbildungen auf konkaven komplexen Räumen. Ann. scient. Éc. Norm. Sup.4e série 20 (1987) 285-310. Zbl0636.32011MR925718
  22. [N] Neeman, A., Ueda theory: Theorems and Problems. AMS Memoirs415 (1989). Zbl0704.32006MR990364
  23. [Og] Ogus, A., The Formal Hodge Filtration. Invent. Math.31 (1976) 193-228. Zbl0339.14004MR401765
  24. [P-S] Peternell, Th. and Schneider, M., Compactification of C3, I. Math. Ann.280 (1988) 129-146. Zbl0651.14025MR928301
  25. [R] Ramis, J.P., Théorèmes de séparation et de finitude pour l'homologie et la cohomologie des espaces (p, q)-convexes-concaves. Ann. Sc. Norm. Sup. Pisa27 (1973) 993-997. Zbl0327.32001MR374477
  26. [R-R 1] Ramis, J.P. and Ruget, G., Complexe dualisant et théorèmes de dualité en géométrie analytique complexe. Publ. Math. I.H.E.S. 38 (1970) 77-91. Zbl0206.25006MR279338
  27. [R-R 2] Ramis, J.P. and Ruget, G., Résidus et dualité. Invent. math.26 (1974) 89-131. Zbl0304.32007MR352522
  28. [R-R-V] Ramis, J.P., Ruget, G., and Verdier, J.L., Dualité relative en géométrie analytique complexe. Invent. Math.13 (1971) 261-283. Zbl0218.14010MR308439
  29. [U] Ueda, T., On the neighborhood of a compact complex curve with topologically trivial normal bundle. J. Math. Kyoto Univ.22 (1983) 583-607. Zbl0519.32019MR685520
  30. [Ue] Ueno, K., Classification theory of algebraic varieties and compact complex spaces. Lecture Notes in Math. vol. 439. Berlin-Heidelberg-New York, Springer1975. Zbl0299.14007MR506253

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