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Proceedings of the American Mathematical Society

Published by the American Mathematical Society since 1950, Proceedings of the American Mathematical Society is devoted to shorter research articles 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 Picard group of a compact flat projective variety
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by N. J. Michelacakis PDF
Proc. Amer. Math. Soc. 124 (1996), 3315-3323 Request permission


In this note, we describe the Picard group of the class of compact, smooth, flat, projective varieties. In view of Charlap’s work and Johnson’s characterization, we construct line bundles over such manifolds as the holonomy-invariant elements of the Neron-Severi group of a projective flat torus covering the manifold. We prove a generalized version of the Appell-Humbert theorem which shows that the nontrivial elements of the Picard group are precisely those coming from the above construction. Our calculations finally give an estimate for the set of positive line bundles for such varieties.
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Additional Information
  • N. J. Michelacakis
  • Affiliation: Rijksuniversiteit Groningen, Afdeling Wiskunde en Informatica, Postbus 800, 9700 AV, Groningen, Netherlands
  • Address at time of publication: 59 Parnithos Street, Vrilissia, 15235 Athens, Greece
  • Received by editor(s): May 22, 1995
  • Communicated by: Peter Li
  • © Copyright 1996 American Mathematical Society
  • Journal: Proc. Amer. Math. Soc. 124 (1996), 3315-3323
  • MSC (1991): Primary 14C22; Secondary 14A10, 14E20
  • DOI:
  • MathSciNet review: 1363429