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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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Lefschetz decompositions for eigenforms on a Kähler manifold
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by Donu Arapura PDF
Proc. Amer. Math. Soc. 146 (2018), 2277-2281 Request permission

Abstract:

We show that the eigenspaces of the Laplacian $\Delta _k$ on $k$-forms on a compact Kähler manifold carry Hodge and Lefschetz decompositions. Among other consequences, we show that the positive part of the spectrum of $\Delta _k$ lies in the spectrum of $\Delta _{k+1}$ for $k<\dim X$.
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Additional Information
  • Donu Arapura
  • Affiliation: Department of Mathematics, Purdue University, West Lafayette, Indiana 47907
  • MR Author ID: 26770
  • Received by editor(s): August 9, 2017
  • Published electronically: February 8, 2018
  • Additional Notes: This research was partially supported by the NSF
  • Communicated by: Lei Ni
  • © Copyright 2018 American Mathematical Society
  • Journal: Proc. Amer. Math. Soc. 146 (2018), 2277-2281
  • MSC (2010): Primary 58J50; Secondary 14C30
  • DOI: https://doi.org/10.1090/proc/14006
  • MathSciNet review: 3767377