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 Varieties with very little transcendental cohomology


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Given a complex algebraic variety X, we define a natural number called the motivic dimension which measures the amount of transcendental cohomology of X. It is zero precisely when all the cohomolgy is spanned by algebraic cycles. Most of this paper is concerned with giving estimates on this number, along with examples where it is small. As an application, we check or recheck the Hodge conjectue in a number of examples: uniruled fourfolds, rationally connected fivefolds, fourfolds fibred by surfaces with p g=0, Hilbert schemes of a small number points on surfaces with p g=0, and generic hypersurfaces.



Author: Donu Arapura

Source: https://archive.org/







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