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A remark on the motive of the Fano variety of lines of a cubic

Research paper by Robert Laterveer

Indexed on: 31 Oct '16Published on: 22 Oct '16Published in: Annales mathématiques du Québec



Abstract

Abstract Let X be a smooth cubic hypersurface, and let F be the Fano variety of lines on X. We establish a relation between the Chow motives of X and F. This relation implies in particular that if X has finite-dimensional motive (in the sense of Kimura), then F also has finite-dimensional motive. This proves finite-dimensionality for motives of Fano varieties of cubics of dimension 3 and 5, and of certain cubics in other dimensions.AbstractLet X be a smooth cubic hypersurface, and let F be the Fano variety of lines on X. We establish a relation between the Chow motives of X and F. This relation implies in particular that if X has finite-dimensional motive (in the sense of Kimura), then F also has finite-dimensional motive. This proves finite-dimensionality for motives of Fano varieties of cubics of dimension 3 and 5, and of certain cubics in other dimensions.XFXXFXF