2002/05/14 by Janós Kollár, János Kollár, Kollár, János
Computer Science · Mathematics · #14C15 #14G27 #14M20 (primary) 14D15 (secondary) #Algebraic Geometry (math.AG) #Algebraic Geometry and Number Theory #Commutative Algebra and Its Applications #FOS: Mathematics #Polynomial and algebraic computation #math.AG #msc:14C15 #msc:14D15 #msc:14G27 #msc:14M20
paper · pdf · doi:10.48550/arxiv.math/0205148
arxiv created 2002/05/14 · openalex publication_date 2002/05/14 · arxiv updated 2009/11/30 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
The paper has two parts. First we prove that the specialization maps on R-equivalence and on the Chow group of zero cycles are isomorphisms for families over a local, Henselian, Dedekind ring when the special fiber is smooth and separably rationally connected. This is pretty much the best one can hope for. The second part contains examples of unirational quartic hypersurfaces whith infinitely many R-equivalence classes. There are also examples of quartics with points in a large odd degree field extension but no points in any smaller odd degree extension.