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DC Field | Value | Language |
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dc.contributor.author | Dvir, Zeev | - |
dc.contributor.author | Hu, G | - |
dc.date.accessioned | 2018-07-20T15:10:28Z | - |
dc.date.available | 2018-07-20T15:10:28Z | - |
dc.date.issued | 2015 | en_US |
dc.identifier.citation | Dvir, Z, Hu, G. (2015). Sylvester-Gallai for Arrangements of Subspaces. 34 (29 - 43. doi:10.4230/LIPIcs.SOCG.2015.29 | en_US |
dc.identifier.uri | http://arks.princeton.edu/ark:/88435/pr19974 | - |
dc.description.abstract | In this work we study arrangements of κ-dimensional subspaces V1, . . . , Vn ⊂ Cl. Our main result shows that, if every pair Va, Vb of subspaces is contained in a dependent triple (a triple Va, Vb, Vc contained in a 2κ-dimensional space), then the entire arrangement must be contained in a subspace whose dimension depends only on k (and not on n). The theorem holds under the assumption that Va \ Vb = {0} for every pair (otherwise it is false). This generalizes the Sylvester-Gallai theorem (or Kelly s theorem for complex numbers), which proves the k = 1 case. Our proof also handles arrangements in which we have many pairs (instead of all) appearing in dependent triples, generalizing the quantitative results of Barak et. al. [1]. One of the main ingredients in the proof is a strengthening of a theorem of Barthe [3] (from the k = 1 to κ>1 case) proving the existence of a linear map that makes the angles between pairs of subspaces large on average. Such a mapping can be found, unless there is an obstruction in the form of a low dimensional subspace intersecting many of the spaces in the arrangement (in which case one can use a different argument to prove the main theorem). | en_US |
dc.format.extent | 29 - 43 | en_US |
dc.language.iso | en_US | en_US |
dc.relation.ispartof | 31st International Symposium on Computational Geometry, SoCG 2015 | en_US |
dc.rights | Author's manuscript | en_US |
dc.title | Sylvester-Gallai for Arrangements of Subspaces | en_US |
dc.type | Conference Article | en_US |
dc.identifier.doi | doi:10.4230/LIPIcs.SOCG.2015.29 | - |
dc.date.eissued | 2015 | en_US |
pu.type.symplectic | http://www.symplectic.co.uk/publications/atom-terms/1.0/conference-proceeding | en_US |
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Sylvester-Gallai for Arrangements of Subspaces.pdf | 230.76 kB | Adobe PDF | View/Download |
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