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arXiv · 2012.04608

Brilliant families of K3 surfaces: Twistor spaces, Brauer groups, and Noether-Lefschetz loci

Daniel Huybrechts
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Abstract

We describe the Hodge theory of brilliant families of K3 surfaces. Their characteristic feature is a close link between the Hodge structures of any two fibres over points in the Noether-Lefschetz locus. Twistor deformations, the analytic Tate-Safarevic group, and one-dimensional Shimura special cycles are covered by the theory. In this setting, the Brauer group is viewed as the Noether-Lefschetz locus of the Brauer family or as the specialization of the Noether-Lefschetz loci in a family of approaching twistor spaces. Passing from one algebraic twistor fibre to another, which by construction is a transcendental operation, is here viewed as first deforming along the more algebraic Brauer family and then along a family of algebraic K3 surfaces.

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Daniel Huybrechts. 2020-12-08. Brilliant families of K3 surfaces: Twistor spaces, Brauer groups, and Noether-Lefschetz loci. https://arxiv.org/abs/2012.04608

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