Dense Algebraic Loci of Hodge Classes

We prove that the Hodge conjecture is equivalent to two statements about abelian varieties, that the locus on which either holds is dense in every family and is the whole family or a meagre set, and that the conjecture holds on every power of the K3 surfaces of the Fricke families of levels 5 and 7.

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Publication Details

Journal
Preprints.org
Published
2026-11-04
DOI
https://doi.org/10.20944/preprints202602.0462.v6
Primary Topic
Algebraic Geometry and Number Theory
Type
preprint
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preprint

Dense Algebraic Loci of Hodge Classes

Deep Bhattacharjee, Ushashi Bhattacharya
Preprints.org
Algebraic Geometry and Number Theory
preprint

Dense Algebraic Loci of Hodge Classes

Deep Bhattacharjee, Ushashi Bhattacharya
preprint en

Abstract

We prove that the Hodge conjecture is equivalent to two statements about abelian varieties, that the locus on which either holds is dense in every family and is the whole family or a meagre set, and that the conjecture holds on every power of the K3 surfaces of the Fricke families of levels 5 and 7.

Preprints.org
Algebraic Geometry and Number Theory
DOIOpen Access PDFOpenAlex
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Dense Algebraic Loci of Hodge Classes — Deep Bhattacharjee, Ushashi Bhattacharya · Preprints.org (2026) | TGRS Research Map | TGRS