Varieties with very little transcendental cohomology - Mathematics > Algebraic GeometryReport as inadecuate




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Abstract: Given a complex algebraic variety X, we define a natural number called themotivic dimension which measures the amount of transcendental cohomology ofX. It is zero precisely when all the cohomolgy is spanned by algebraiccycles. 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 recheckthe Hodge conjectue in a number of examples: uniruled fourfolds, rationallyconnected fivefolds, fourfolds fibred by surfaces with p g=0, Hilbert schemesof a small number points on surfaces with p g=0, and generic hypersurfaces.



Author: Donu Arapura

Source: https://arxiv.org/







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