Artykuł w czasopiśmie
Brak miniatury
Licencja
A very special EPW sextic and two IHS fourfolds
Autor
Data publikacji
2017
Abstrakt (EN)
We 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.
Dyscyplina PBN
matematyka
Czasopismo
Geometry and Topology
Tom
21
Zeszyt
2
Strony od-do
1179-1230
ISSN
1465-3060
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