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Proceedings of the American Mathematical Society

Published by the American Mathematical Society, the Proceedings of the American Mathematical Society (PROC) is devoted to research articles of the highest quality in all areas of pure and applied mathematics.

ISSN 1088-6826 (online) ISSN 0002-9939 (print)

The 2020 MCQ for Proceedings of the American Mathematical Society is 0.85.

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On the infinite dimensionality of the Dolbeault cohomology groups
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by Henry B. Laufer PDF
Proc. Amer. Math. Soc. 52 (1975), 293-296 Request permission

Abstract:

Let $M$ be an open subset of a Stein manifold without isolated points. Let ${\Omega ^p}$ be the sheaf of germs of holomorphic $p$-forms on $M$. Then ${H^q}(M,{\Omega ^p})$ is either $0$ or else infinite dimensional. ${H^q}(M,\mathcal {S})$ may be nonzero and finite dimensional if $M$ is the regular points of a Stein space or if $\mathcal {S}$ is an arbitrary coherent sheaf over $M$.
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Additional Information
  • © Copyright 1975 American Mathematical Society
  • Journal: Proc. Amer. Math. Soc. 52 (1975), 293-296
  • MSC: Primary 32C35
  • DOI: https://doi.org/10.1090/S0002-9939-1975-0379887-2
  • MathSciNet review: 0379887