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A very special EPW sextic and two IHS fourfolds

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dc.abstract.enWe show that the Hilbert scheme of two points on the Vinberg K3 surface has a two-to-one map onto a very symmetric EPW sextic Y in P5. The fourfold Y is singular along 60 planes, 20 of which form a complete family of incident planes. This solves a problem of Morin and O’Grady and establishes that 20 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 X0 constructed by Donten-Bury and Wiśniewski [On 81 symplectic resolutions of a 4–dimensional quotient by a group of order 32, preprint (2014)]. We find that X0 is also related to the Debarre–Varley abelian fourfold.
dc.affiliationUniwersytet Warszawski
dc.contributor.authorDonten-Bury, Maria
dc.contributor.authorKapustka, Grzegorz
dc.contributor.authorKapustka, Michał
dc.contributor.authorGeemen, Bert van
dc.contributor.authorWiśniewski, Jarosław
dc.date.accessioned2024-01-24T18:14:22Z
dc.date.available2024-01-24T18:14:22Z
dc.date.issued2017
dc.description.financeNie dotyczy
dc.description.number2
dc.description.volume21
dc.identifier.doi10.2140/GT.2017.21.1179
dc.identifier.issn1465-3060
dc.identifier.urihttps://repozytorium.uw.edu.pl//handle/item/101930
dc.languageeng
dc.pbn.affiliationmathemathics
dc.relation.ispartofGeometry and Topology
dc.relation.pages1179-1230
dc.rightsClosedAccess
dc.sciencecloudnosend
dc.titleA very special EPW sextic and two IHS fourfolds
dc.typeJournalArticle
dspace.entity.typePublication