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Journal of the American Mathematical Society

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

ISSN 1088-6834 (online) ISSN 0894-0347 (print)

The 2020 MCQ for Journal of the American Mathematical Society is 4.79.

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The Dolbeault complex in infinite dimensions I
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by László Lempert PDF
J. Amer. Math. Soc. 11 (1998), 485-520 Request permission

Abstract:

In this paper we introduce certain basic notions concerning infinite dimensional complex manifolds, and prove that the Dolbeault cohomology groups of infinite dimensional projective spaces, with values in finite rank vector bundles, vanish. Some applications of such vanishing theorems are discussed; e.g., we classify vector bundles of finite rank over infinite dimensional projective spaces. Finally, we prove a sharp theorem on solving the inhomogeneous Cauchy–Riemann equations on affine spaces.
References
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Additional Information
  • László Lempert
  • Affiliation: Department of Mathematics, Purdue University, West Lafayette, Indiana 47907
  • MR Author ID: 112435
  • Email: lempert@math.purdue.edu
  • Received by editor(s): February 4, 1997
  • Additional Notes: This research was partially supported by an NSF grant, and also by the Mathematical Sciences Research Institute, Berkeley.
  • © Copyright 1998 American Mathematical Society
  • Journal: J. Amer. Math. Soc. 11 (1998), 485-520
  • MSC (1991): Primary 32C10, 32L20, 58B12
  • DOI: https://doi.org/10.1090/S0894-0347-98-00266-5
  • MathSciNet review: 1603858