Some non-pseudoconvex domains with explicitly computable non-Hausdorff Dolbeault cohomology

详细信息    查看全文

• 作者：Debraj Chakrabarti
• 关键词：32C35 ; Dolbeaut cohomology ; non ; Hausdorff topologies
• 刊名：Archiv der Mathematik
• 出版年：2015
• 出版时间：December 2015
• 年：2015
• 卷：105
• 期：6
• 页码：571-584
• 全文大小：560 KB
• 参考文献：1.Cassa A.: Coomologia separata sulle variet脿 analitiche complesse. Ann. Scuola Norm. Sup. Pisa (3) 25, 291鈥?23 (1971)MATH MathSciNet
  2.J.-P. Demailly. Diff茅rents exemples de fibr茅s holomorphes non de Stein. In S茅minaire Pierre Lelong-Henri Skoda (Analyse), Ann茅e 1976/77, volume 694 of Lecture Notes in Math., pages 15鈥?1. Springer, Berlin, 1978.
  3.Fritzsche K., Grauert H.: From holomorphic functions to complex manifolds, volume 213 of Graduate Texts in Mathematics. Springer-Verlag, New York (2002)CrossRef
  4.P. Griffiths and J. Harris. Principles of algebraic geometry. Wiley-Interscience, New York, 1978. Pure and Applied Mathematics.
  5.H. Grauert and R. Remmert. Theory of Stein spaces. Classics in Mathematics. Springer-Verlag, Berlin, 2004. Translated from the German by Alan Huckleberry, Reprint of the 1979 translation.
  6.R. C. Gunning and H. Rossi. Analytic functions of several complex variables. AMS Chelsea Publishing, Providence, RI, 2009. Reprint of the 1965 original.
  7.J. L. Kelley and Isaac Namioka. Linear topological spaces. Springer-Verlag, New York-Heidelberg, 1976. Second corrected printing, Graduate Texts in Mathematics, No. 36.
  8.Laufer H. B.: On Serre duality and envelopes of holomorphy. Trans. Am. Math. Soc. 128, 414鈥?36 (1967)MATH MathSciNet CrossRef
  9.Laufer Henry B.: On the infinite dimensionality of the Dolbeault cohomology groups. Proc. Am. Math. Soc. 52, 293鈥?96 (1975)MATH MathSciNet CrossRef
  10.Laurent-Thi茅baut C., Shaw Mei-Chi.: On the Hausdorff property of some Dolbeault cohomology groups. Math. Z. 274(3鈥?), 1165鈥?176 (2013)MATH MathSciNet CrossRef
  11.B. Malgrange. La cohomologie d鈥檜ne vari茅t茅 analytique complexe 脿 bord pseudo-convexe n鈥檈st pas n茅cessairement s茅par茅e. C. R. Acad. Sci. Paris S茅r. A-B, 280:Aii, A93鈥揂95, 1975.
  12.J.-P. Serre.: Un th茅or猫me de dualit茅. Comment. Math. Helv. 29, 9鈥?6 (1955)MathSciNet CrossRef
  13.Siu Y.-T.: Non-countable dimensions of cohomology groups of analytic sheaves and domains of holomorphy. Math. Z. 102, 17鈥?9 (1967)MATH MathSciNet CrossRef
  14.Trapani S.: Envelopes of holomorphy and Hausdorff cohomology groups. Rend. Sem. Mat. Univ. Padova 75, 25鈥?7 (1986)MATH MathSciNet
  15.Tr猫ves F.: Topological vector spaces, distributions and kernels. Academic Press, New York-London (1967)MATH
  
• 作者单位：Debraj Chakrabarti (1)
  
  1. Central Michigan University, Mt. Pleasant, MI, 48859, USA
  
• 刊物类别：Mathematics and Statistics
• 刊物主题：Mathematics
  Mathematics
  
• 出版者：Birkh盲user Basel
• ISSN：1420-8938

文摘

We explicitly compute the Dolbeault cohomologies of certain domains in complex space generalizing the classical Hartogs figure. The cohomology groups are non-Hausdorff topological vector spaces, and it is possible to identify the reduced (Hausdorff) and the indiscrete part of the cohomology. Keywords Dolbeaut cohomology non-Hausdorff topologies