The hodge theory of flat vector bundles on a complex torus
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. © 1982 American Mathematical Society.
Publication Source (Journal or Book title)
Transactions of the American Mathematical Society
William Hoffman, J. (1982). The hodge theory of flat vector bundles on a complex torus. Transactions of the American Mathematical Society, 271 (1), 117-131. https://doi.org/10.1090/S0002-9947-1982-0648081-8