Hyper-Kähler fourfolds and Grassmann geometry

Abstract

We construct a new 20-dimensional family of algebraic hyper-Kaehler fourfolds and prove that they are deformation-equivalent to the second punctual Hilbert scheme of a K3 surface of degree 22.

Typos corrected. Connection made with the work of Gritsenko, Hulek, and Sankaran on the Kodaira dimension of moduli spaces of hyper-Kaehler manifolds (arXiv:0802.2078)

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• Fano manifolds of degree ten and EPW sextics
• Smooth Surfaces in Smooth Fourfolds with Vanishing First Chern Class
• Complete intersection hyperkähler fourfolds with respect to equivariant vector bundles over rational homogeneous varieties of Picard number one