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 P-5. 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 X-0 constructed by Donten-Bury and Wisniewski [On 81 symplectic resolutions of a 4-dimensional quotient by a group of order 32, preprint (2014)]. We find that X-0 is also related to the Debarre-Varley abelian fourfold.
A very special EPW sextic and two IHS fourfolds / M. Donten-Bury, B. van Geemen, G. Kapustka, M. Kapustka, J. Wiśniewski. - In: GEOMETRY & TOPOLOGY. - ISSN 1364-0380. - 21:2(2017), pp. 1179-1230.
|Titolo:||A very special EPW sextic and two IHS fourfolds|
VAN GEEMEN, LAMBERTUS (Secondo)
|Parole Chiave:||surfaces; varieties; manifolds|
|Settore Scientifico Disciplinare:||Settore MAT/03 - Geometria|
|Data di pubblicazione:||2017|
|Digital Object Identifier (DOI):||http://dx.doi.org/10.2140/gt.2017.21.1179|
|Appare nelle tipologie:||01 - Articolo su periodico|