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Transactions of the American Mathematical Society

ISSN 1088-6850(online) ISSN 0002-9947(print)



The Hodge theory of flat vector bundles on a complex torus

Author: Jerome William Hoffman
Journal: Trans. Amer. Math. Soc. 271 (1982), 117-131
MSC: Primary 32J25; Secondary 10F35, 14C30, 14K20, 32L20
MathSciNet review: 648081
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Abstract: We study the Hodge spectral sequence of a local system on a compact, complex torus by means of the theory of harmonic integrals. It is shown that, in some cases, Baker's theorems concerning linear forms in the logarithms of algebraic numbers may be applied to obtain vanishing theorems in cohomology. This is applied to the study of Betti and Hodge numbers of compact analytic threefolds which are analogues of hyperelliptic surfaces. Among other things, it is shown that, in contrast to the two-dimensional case, some of these varieties are nonalgebraic.

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Article copyright: © Copyright 1982 American Mathematical Society