Correspondences for hyperk\"ahler varieties with large Picard numbers

Ljudmila Kamenova; Abhinav Kumar

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arXiv · 2607.09622

Correspondences for hyperk\"ahler varieties with large Picard numbers

Ljudmila Kamenova·Abhinav Kumar

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Abstract

In this note, we explore the connection between hyperk\"ahler manifolds with large Picard numbers and abelian varieties. In particular, we are interested in Morrison's solution to the (modified) Oda's conjecture: every K3 surface whose Picard group is large enough (in a certain precise sense) must be related via an algebraic correspondence to an abelian surface. We generalize this theorem to the case of known examples of hyperk\"ahler manifolds such as pointed Hilbert schemes on K3 surfaces.

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BibTeX RIS

Ljudmila Kamenova, Abhinav Kumar. 2026-07-10. Correspondences for hyperk\"ahler varieties with large Picard numbers. https://arxiv.org/abs/2607.09622

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