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arXiv · 1611.08818

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

Robert Laterveer
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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.

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Robert Laterveer. 2016-11-27. A remark on the motive of the Fano variety of lines of a cubic. https://doi.org/10.1007/s40316-016-0070-x

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