Journal of Algebraic Geometry

Journal of Algebraic Geometry

Online ISSN 1534-7486; Print ISSN 1056-3911

   
 
 

 

Motives and representability of algebraic cycles on threefolds over a field


Authors: Sergey Gorchinskiy and Vladimir Guletskiĭ
Journal: J. Algebraic Geom. 21 (2012), 347-373
DOI: https://doi.org/10.1090/S1056-3911-2011-00548-1
Published electronically: May 31, 2011
Corrigendum: J. Algebraic Geom. 22 (2013), 795-796.
MathSciNet review: 2877438
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Abstract | References | Additional Information

Abstract: We study algebraic cycles on threefolds and finite-dimensionality of their motives with coefficients in $\mathbb Q$. We decompose the motive of a non-singular projective threefold $X$ with representable algebraic part of $CH_0(X)$ into Lefschetz motives and the Picard motive of a certain abelian variety, isogenous to the Griffiths’ intermediate Jacobian $J^2(X)$ when the ground field is $\mathbb C$. In particular, it implies motivic finite-dimensionality of Fano threefolds over a field. We also prove representability of zero-cycles on several classes of threefolds fibred by surfaces with algebraic $H^2$. This gives new examples of three-dimensional varieties whose motives are finite-dimensional.


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Sergey Gorchinskiy
Affiliation: Steklov Mathematical Institute, Gubkina str. 8, 119991, Moscow, Russia
MR Author ID: 786536
Email: gorchins@mi.ras.ru

Vladimir Guletskiĭ
Affiliation: Department of Mathematical Sciences, University of Liverpool, Peach Street, Liverpool L69 7ZL, England, United Kingdom
Email: vladimir.guletskii@liverpool.ac.uk

Received by editor(s): July 3, 2009
Received by editor(s) in revised form: September 21, 2009
Published electronically: May 31, 2011
Additional Notes: The first author was partially supported by the grants RFBR 08-01-00095, NSh-1987.2008.1 and MK-297.2009.1.