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A very special EPW sextic and two IHS fourfolds
We show that the Hilbert scheme of two points on the Vinberg surface has
a 2:1 map onto a very symmetric EPW sextic in . The fourfold
is singular along planes, of which form a complete family of
incident planes. This solves a problem of Morin and O'Grady and establishes
that is the maximal cardinality of such a family of planes. Next, we show
that this Hilbert scheme is birationally isomorphic to the Kummer type IHS
fourfold constructed in [DW]. We find that is also related to the
Debarre-Varley abelian fourfold.Comment: 32 page
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