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Motives of hypersurfaces of very small degree

Author: Andre Chatzistamatiou
Journal: Proc. Amer. Math. Soc. 138 (2010), 435-444
MSC (2000): Primary 14-XX
Published electronically: October 5, 2009
MathSciNet review: 2557161
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Abstract: We study the Chow motive (with rational coefficients) of a hypersurface $ X$ in the projective space by using the variety $ F(X)$ of $ l$-dimensional planes contained in $ X$. If the degree of $ X$ is sufficiently small, we show that the primitive part of the motive of $ X$ is the tensor product of a direct summand in the motive of a suitable complete intersection in $ F(X)$ and the $ l$-th twist $ \mathbb{Q} (-l)$ of the Lefschetz motive.

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Additional Information

Andre Chatzistamatiou
Affiliation: Fachbereich Mathematik, Universität Duisburg-Essen, 45117 Essen, Germany

Received by editor(s): January 18, 2008
Received by editor(s) in revised form: April 27, 2009
Published electronically: October 5, 2009
Additional Notes: The author was supported by a fellowship within the Post-Doc program of the Deutsche Forschungsgemeinschaft (DFG)
Communicated by: Ted Chinburg
Article copyright: © Copyright 2009 American Mathematical Society