2014/05/25 by Kalyan Banerjee, Banerjee, Kalyan, Vladimir Guletskiĭ +1 · 1 citation
Mathematics · #14C25 #14D05 #14F30 #14J30 #14J35 #Advanced Differential Equations and Dynamical Systems #Algebraic Geometry (math.AG) #Algebraic Geometry and Number Theory #FOS: Mathematics #Meromorphic and Entire Functions
paper · pdf · doi:10.48550/arxiv.1405.6430
openalex publication_date 2014/05/25 · openalex created_date 2022/08/15 · openalex updated_date 2026/07/28
Let k be an uncountable algebraically closed field of characteristic 0,\nand let X be a smooth projective connected variety of dimension 2p,\nappropriately embedded into mathbb Pm over k. Let Y be a hyperplane\nsection of X, and let Ap(Y) and Ap+1(X) be the groups of\nalgebraically trivial algebraic cycles of codimension p and p+1 modulo\nrational equivalence on Y and X respectively. Assume that, whenever Y is\nsmooth, the group Ap(Y) is regularly parametrized by an abelian variety A\nand coincides with the subgroup of degree 0 classes in the Chow group\nCHp(Y). In the paper we prove that the kernel of the push-forward\nhomomorphism from Ap(Y) to Ap+1(X) is the union of a countable\ncollection of shifts of a certain abelian subvariety A0 inside A. For a\nvery general section Y either A0=0 or A0 coincides with an abelian\nsubvariety A1 in A whose tangent space is the group of vanishing cycles\nH2p-1(Y) rm van. Then we apply these general results to sections of a\nsmooth cubic fourfold in mathbb P5.\n