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Title: On the Picard group of a compact flat projective variety
Keywords: Appell-Humbert theorem
Bieberbach group
cohomology of groups
complex structure
group action
global section of line bundle
group representation
flat Riemannian manifold
holonomy group
Lyndon-Hotschild-Serre spectral sequence
Lefschetz's theorem
Lie group
(ample) line bundle
Neron-Severi group
Picard group
Issue Date: 1996
Publisher: American Mathematical Society
Citation: Proceedings of the American Mathematical Society 124 (1996), 3315-3323
Abstract: 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.
ISSN: 1088-6826
Appears in Collections:Δημοσιεύσεις σε Περιοδικά

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