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

  • Salvatore Floccari
  • Lie Fu
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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.

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Cite

BibTeXRIS
BibTeX
@misc{floccari2026hodge,
  title = {{On the Hodge conjecture for hyper-Kähler varieties of generalized Kummer type of dimension divisible by four}},
  author = {Salvatore Floccari and Lie Fu},
  howpublished = {arXiv},
  year = {2026},
  month = oct,
  doi = {10.48550/arxiv.2610.31740},
  eprint = {2610.31740},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2610.31740},
}
RIS
TY  - UNPB
TI  - On the Hodge conjecture for hyper-Kähler varieties of generalized Kummer type of dimension divisible by four
AU  - Salvatore Floccari
AU  - Lie Fu
PY  - 2026
DA  - 2026/10/22
PB  - arXiv
DO  - 10.48550/arxiv.2610.31740
UR  - https://arxiv.org/abs/2610.31740
AB  - 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.
ER  -