Journal of Algebraic Geometry

Journal of Algebraic Geometry

Online ISSN 1534-7486; Print ISSN 1056-3911



$ R$-equivalence on low degree complete intersections

Author: Alena Pirutka
Journal: J. Algebraic Geom. 21 (2012), 707-719
Published electronically: November 9, 2011
MathSciNet review: 2957693
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Abstract: Let $ k$ be a function field in one variable over $ \mathbb{C}$ or the field $ \mathbb{C}((t))$. Let $ X$ be a $ k$-rationally simply connected variety defined over $ k$. In this paper we show that $ R$-equivalence on rational points of $ X$ is trivial and that the Chow group of zero-cycles of degree zero $ A_0(X)$ is zero. In particular, this holds for a smooth complete intersection of $ r$ hypersurfaces in $ \mathbb{P}^n_k$ of respective degrees $ d_1,\ldots ,d_r$ with $ \sum \limits _{i=1}^{r}d_i^2\leq n+1$.

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Alena Pirutka
Affiliation: École Normale Supérieure, 45 rue d’Ulm, 75230 Paris Cedex 05, France

Received by editor(s): December 4, 2009
Received by editor(s) in revised form: November 23, 2010
Published electronically: November 9, 2011

American Mathematical Society