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dc.contributor.authorPokora, Piotr
dc.contributor.authorSzemberg, Tomasz
dc.contributor.authorSzpond, Justyna
dc.date.accessioned2020-10-07T13:11:26Z
dc.date.available2020-10-07T13:11:26Z
dc.date.issued2020-10-07
dc.identifier.urihttp://publications.mfo.de/handle/mfo/3799
dc.description.abstractFelix Klein in course of his study of the regular and its symmetries encountered a highly symmetric configuration of 60 points in $\mathbb{P}^3$. This configuration has appeared in various guises, perhaps post notably as the configuration of points dual to the 60 reflection planes in the group $G_{31}$ in the Shephard-Todd list. In the present note we show that the 60 points exhibit interesting properties relevant from the point of view of two paths of research initiated recently. Firstly, they give rise to two completely different unexpected surfaces of degree 6. Unexpected hypersurfaces have been introduced by Cook II, Harbourne, Migliore, Nagel in 2018. One of unexpected surfaces associated to the configuration of 60 points is a cone with a single singularity of multiplicity 6 and the other has three singular points of multiplicities 4; 2 and 2. Secondly, Chiantini and Migliore observed in 2020 that there are non-trivial sets of points in $\mathbb{P}^3$ with the surprising property that their general projection to $\mathbb{P}^2$ is a complete intersection. They found a family of such sets, which they called grids. An appendix to their paper describes an exotic configuration of 24 points in $\mathbb{P}^3$ which is not a grid but has the remarkable property that its general projection is a complete intersection. We show that the Klein configuration is also not a grid and it projects to a complete intersections. We identify also its proper subsets, which enjoy the same property.en_US
dc.language.isoen_USen_US
dc.publisherMathematisches Forschungsinstitut Oberwolfachen_US
dc.relation.ispartofseriesOberwolfach Preprints;2020,19
dc.subjectBase locien_US
dc.subjectConesen_US
dc.subjectComplete intersectionsen_US
dc.subjectFinite Heisenberg groupen_US
dc.subjectKlein configurationen_US
dc.subjectProjectionsen_US
dc.subjectReflection groupen_US
dc.subjectSpecial linear systemsen_US
dc.subjectUnexpected hypersurfacesen_US
dc.titleUnexpected Properties of the Klein Configuration of 60 Points in $\mathbb{P}^3$en_US
dc.typePreprinten_US
dc.identifier.doi10.14760/OWP-2020-19
local.scientificprogramResearch in Pairs 2020en_US
local.series.idOWP-2020-19en_US
local.subject.msc14en_US
local.subject.msc13en_US


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