# Families of hyperk\\"ahler manifolds

Source: [Families of hyperk\\"ahler manifolds](<https://www.sota2.com/research/paper/68fa4d0f1e209131ce951e46>)

Collection index: [llms.txt](<https://www.sota2.com/research/llms.txt>)

Data updated: 2025-10-25T09:08:30.993Z

Authors: K. Oguiso

Published: 1999-11-15T13:34:44.000Z

## Abstract

We show the density of the jumping loci of the Picard number of a hyperk\\"ahler manifold under small deformation and provide several applications. In particular, we apply this to reveal the structure of hierarchy among all the narrow Mordell-Weil lattices of Jacobian K3 surfaces.

## Recorded benchmark results

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## Original sources and implementation

[Original paper](<https://arxiv.org/abs/math/9911105>)

[PDF](<https://arxiv.org/pdf/math/9911105.pdf>)