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2021 Albanese kernels and Griffiths groups
Bruno Kahn
Tunisian J. Math. 3(3): 589-656 (2021). DOI: 10.2140/tunis.2021.3.589

Abstract

We describe the Griffiths group of the product of a curve C and a surface S as a quotient of the Albanese kernel of S over the function field of C. When C is a hyperplane section of S varying in a Lefschetz pencil, we prove the nonvanishing in Griff(C×S) of a modification of the graph of the embedding CS for infinitely many members of the pencil, provided the ground field k is of characteristic 0, the geometric genus of S is >0, and k is large or S is “of motivated abelian type”.

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Bruno Kahn. "Albanese kernels and Griffiths groups." Tunisian J. Math. 3 (3) 589 - 656, 2021. https://doi.org/10.2140/tunis.2021.3.589

Information

Received: 22 April 2020; Revised: 12 August 2020; Accepted: 26 August 2020; Published: 2021
First available in Project Euclid: 25 June 2021

Digital Object Identifier: 10.2140/tunis.2021.3.589

Subjects:
Primary: 14C25, 14D06

Rights: Copyright © 2021 Mathematical Sciences Publishers

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Vol.3 • No. 3 • 2021
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