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Abstract
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We describe the Griffiths group of the product of a curve
and a surface
as a quotient of the
Albanese kernel of
over
the function field of
.
When
is a
hyperplane section of
varying in a Lefschetz pencil, we prove the nonvanishing in
Griff
of a modification of the graph of the embedding
for infinitely many members of the pencil, provided the ground field
is of characteristic
, the geometric
genus of
is
,
and
is
large or
is “of motivated abelian type”.
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Keywords
Albanese kernel, Griffiths group, motive
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Mathematical Subject Classification
Primary: 14C25, 14D06
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Milestones
Received: 22 April 2020
Revised: 12 August 2020
Accepted: 26 August 2020
Published: 13 May 2021
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