Algebraic cycles on hyper-K\"ahler varieties of generalized Kummer type

Salvatore Floccari; Mauro Varesco

doi:10.1007/s00208-024-03027-z

Algebraic cycles on hyper-K\"ahler varieties of generalized Kummer type

Algebraic Geometry 2024-11-13 v2

Authors: Salvatore Floccari , Mauro Varesco

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Abstract

We prove the conjectures of Hodge and Tate for any four-dimensional hyper-K\"ahler variety of generalized Kummer type. For an arbitrary variety $X$ of generalized Kummer type, we show that all Hodge classes in the subalgebra of the rational cohomology generated by $H^2(X,\mathbb{Q})$ are algebraic.

Keywords

algebraic cycles hyper-kahler varieties generalized kummer type hodge conjecture tate conjecture hodge classes

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@article{arxiv.2308.04865,
  title  = {Algebraic cycles on hyper-K\"ahler varieties of generalized Kummer type},
  author = {Salvatore Floccari and Mauro Varesco},
  journal= {arXiv preprint arXiv:2308.04865},
  year   = {2024}
}

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v2: final version, published on Mathematische Annalen

Algebraic cycles on hyper-K\"ahler varieties of generalized Kummer type

Abstract

Keywords

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