Kuga–Satake Construction on Families of K3 Surfaces of Picard Rank 14

Flora Poon

doi:10.1002/mana.70173

Kuga–Satake Construction on Families of K3 Surfaces of Picard Rank 14

Flora Poon

Department of Mathematical Sciences

Research output: Contribution to journal › Article › peer-review

Abstract

The isometry between the type IV₆ and the type II₄ hermitian symmetric domains suggests a possible relation between suitable moduli spaces of K3 surfaces of Picard rank 14 and of polarized abelian 8-folds with totally definite quaternion multiplication. We show how this isometry induces a geometrically meaningful map between such moduli spaces using the Kuga–Satake construction. Furthermore, we illustrate how the modular mapping can be realized for some specific families of K3 surfaces of Picard rank 14, which can be specialized to families of K3 surfaces of higher Picard rank.

Original language	English
Article number	370173
Journal	Mathematische Nachrichten
Early online date	4 Jun 2026
DOIs	https://doi.org/10.1002/mana.70173
Publication status	E-pub ahead of print - 4 Jun 2026

Data Availability Statement

Data sharing is not applicable to this paper as no datasets were generated or analyzed during the current study.

Funding

EPSRC. Grant Number: EP/V520305/1

Keywords

abelian varieties
coarse moduli spaces
K3 surfaces
Kuga–Satake construction

ASJC Scopus subject areas

General Mathematics

Access to Document

10.1002/mana.70173Licence: CC BY

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abstract = "The isometry between the type IV6 and the type II4 hermitian symmetric domains suggests a possible relation between suitable moduli spaces of K3 surfaces of Picard rank 14 and of polarized abelian 8-folds with totally definite quaternion multiplication. We show how this isometry induces a geometrically meaningful map between such moduli spaces using the Kuga–Satake construction. Furthermore, we illustrate how the modular mapping can be realized for some specific families of K3 surfaces of Picard rank 14, which can be specialized to families of K3 surfaces of higher Picard rank.",

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Kuga–Satake Construction on Families of K3 Surfaces of Picard Rank 14

Abstract

Data Availability Statement

Funding

Keywords

ASJC Scopus subject areas

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