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On the Hodge conjecture for hyper-Kähler varieties of generalized Kummer type of dimension divisible by four

Year: 2026

Type: preprint

Abstract: We prove the Hodge conjecture for all hyper-Kähler varieties of generalized Kummer type of dimension $2n$ with $n+1$ a prime number, and all powers of these varieties. For any variety $X$ of generalized Kummer type of dimension divisible by 4, we show that the Lefschetz standard conjecture for $X$ implies the Hodge conjecture for $X$ and all its powers.

Source: arXiv (Cornell University)

DOI: 10.48550/arxiv.2610.31740

Authors: Floccari, Salvatore, Fu, Lie

Language: English

Topic: Algebraic Geometry and Number Theory

Subfield: Geometry and Topology

Field: Mathematics

Domain: Physical Sciences

Open Access status: green

Funders: Agence Nationale de la Recherche, Université de Strasbourg, Centre National de la Recherche Scientifique, Institut Universitaire de France

Awards: Derived algebraic geometry applied to representation theory and singularities of schemes, G3311816218, G5296751580, From Fano to hyperKähler varieties: geometry and derived categories

OpenAlex ID: W7223673986

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