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A
very special EPW sextic and two IHS fourfolds
Maria Donten-Bury, Bert van Geemen, Grzegorz Kapustka, Michał Kapustka and Jarosław A Wiśniewski |
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Geometry & Topology 21 (2017) 1179–1230
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Abstract |
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We show that the Hilbert scheme of two points on the Vinberg surface has a two-to-one 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 by Donten-Bury and Wiśniewski [On 81 symplectic resolutions of a 4–dimensional quotient by a group of order , preprint (2014)]. We find that is also related to the Debarre–Varley abelian fourfold. |
Keywords
EPW sextics, IHS fourfolds, abelian varieties
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Mathematical Subject Classification 2010
Primary: 14D06, 14J35, 14J70, 14K12, 14M07
Secondary: 14J50, 14J28
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References |
Publication
Received: 28 September 2015
Revised: 28 January 2016
Accepted: 3 March 2016
Published: 17 March 2017
Proposed: Richard Thomas
Seconded: Jim Bryan, Simon Donaldson
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Authors |
| Maria Donten-Bury | |
| Institute of Mathematics Freie Universität Berlin Arnimallee 3 D-14195 Berlin Germany |
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| Bert van Geemen | |
| Department of Mathematics University di Milano I-20133 Milan Italy |
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| Grzegorz Kapustka | |
| Institute of Mathematics of the
Polish Academy of Sciences ul. Sniadeckich 8 P.O. Box 21 00-656 Warszawa Poland |
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| Michał Kapustka | |
| Department of Mathematics and
Informatics Jagiellonian University Łojasiewicza 6 30-348 Kraków Poland |
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| Jarosław A Wiśniewski | |
| Faculty of Mathematics Informatics and Mechanics University of Warsaw Banacha 2 02-097 Warszawa Poland |
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