The Hodge Conjecture for Powers of K3 Surfaces of Picard Number 16

We study the Hodge conjecture for powers of K3 surfaces and show that if the Kuga–Satake correspondence is algebraic for a family of K3 surfaces of generic Picard number 16, then the Hodge conjecture holds for all powers of any K3 surface in that family.

Publication Details

Journal
The Michigan Mathematical Journal
Published
2024-09-23
DOI
https://doi.org/10.1307/mmj/20236349
Primary Topic
Algebraic Geometry and Number Theory
Type
article
Field-Weighted Citation Impact
0.00
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article

The Hodge Conjecture for Powers of K3 Surfaces of Picard Number 16

The Michigan Mathematical Journal
Algebraic Geometry and Number Theory
article

The Hodge Conjecture for Powers of K3 Surfaces of Picard Number 16

article en

Abstract

We study the Hodge conjecture for powers of K3 surfaces and show that if the Kuga–Satake correspondence is algebraic for a family of K3 surfaces of generic Picard number 16, then the Hodge conjecture holds for all powers of any K3 surface in that family.

The Michigan Mathematical JournalVol. 75(5)
Openalex Percentile: Top 98%
Algebraic Geometry and Number Theory
DOISourceOpenAlex
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The Hodge Conjecture for Powers of K3 Surfaces of Picard Number 16 · The Michigan Mathematical Journal (2024) | TGRS Research Map | TGRS