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Author(s): Bhargava, Manjul; Ho, Wei; Kumar, Abhinav

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Abstract: We study moduli spaces of lattice-polarized K3 surfaces in terms of orbits of representations of algebraic groups. In particular, over an algebraically closed field of characteristic 0, we show that in many cases, the nondegenerate orbits of a representation are in bijection with K3 surfaces (up to suitable equivalence) whose Néron–Severi lattice contains a given lattice. An immediate consequence is that the corresponding moduli spaces of these lattice-polarized K3 surfaces are all unirational. Our constructions also produce many fixed-point-free automorphisms of positive entropy on K3 surfaces in various families associated to these representations, giving a natural extension of recent work of Oguiso.
Publication Date: 7-Jul-2016
Citation: Bhargava, Manjul, Ho, Wei, Kumar, Abhinav. (2016). ORBIT PARAMETRIZATIONS FOR K3 SURFACES. FORUM OF MATHEMATICS SIGMA, 4, doi:10.1017/fms.2016.12
DOI: doi:10.1017/fms.2016.12
ISSN: 2050-5094
Pages: 1 - 86
Type of Material: Journal Article
Journal/Proceeding Title: FORUM OF MATHEMATICS SIGMA
Version: Final published version. This is an open access article.

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