Lagrangian tens of planes, Enriques surfaces and holomorphic symplectic fourfolds

Igor Dolgachev, Dimitri Markushevich

Published 2019-06-04Version 1

Fano models of Enriques surfaces in $\mathbb P^5$. The first one parametrizes the varieties of lines on smooth cubic hypersurfaces containing 10 mutually intersecting planes. The second one is a family of double EPW sextics introduced by K. O'Grady. The EPW sextics are associated to Lagrangian subspaces of the Pl\"ucker space of the Grassmannian $G_2(\mathbb P^5)$ spanned by 10 mutually intersecting planes in $\mathbb P^5$. Also some results are obtained on the variety of general tens of mutually intersecting planes, not necessarily associated to Fano models of Enriques surfaces.