R-equivalence on low degree complete intersections

2009/07/11 by Pirutka, Alena
#14C15 #14G05 #14N25 #Algebraic Geometry (math.AG) #FOS: Mathematics

paper · doi:10.48550/arxiv.0907.1971

Abstract

Let k be the function field of a complex curve or the field C((t)). We show that for a smooth complete intersection X of r hypersurfaces in Pⁿ_k of respective degrees d₁,...,d_r with ∑ d_i²≤ n+1 the R-equivalence on rational points of X is trivial and the Chow group of zero-cycles of degree zero A₀(X) is zero.

Related

• On the arithmetic of weighted complete intersections of low degree
• Rationally connected varieties over finite fields
• Geometry of Rational Curves on Low degree Complete Intersections
• A remark on the product by the hyperplane class in the Chow ring of some complete intersections
• Rational curves on complete intersections and the circle method