Type: Article
Publication Date: 1974-07-01
Citations: 65
DOI: https://doi.org/10.2140/pjm.1974.53.281
In this paper it is shown that if π:X->X is a proper holomorphic surjection of equidimensional complex manifolds then the induced mapping π*: H q (X, Ω\) -» H Q (X, Ω\) on Dolbeault groups is injective.As a consequence one obtains the inequality h p ' 9 (X) g h p -9 (X) for the Hodge numbers of X and X.This result is valid also in the case of vector bundle coefficients, and can be generalized to the case of nondiscrete fibres of the mapping π (non equidimensional case) by the imposition of a Kahlerian condition on X. Corresponding results for differentiate mappings are formulated and proved.Illustrative examples are provided to show the necessity of the various assumptions made.