dc.date.accessioned | 2017-12-15T16:08:29Z | |
dc.date.available | 2017-12-15T16:08:29Z | |
dc.date.created | 2016-09-05T15:39:04Z | |
dc.date.issued | 2017 | |
dc.identifier.citation | Ranestad, Kristian Mezzetti, Emilia De Poi, Pietro Faenzi, Daniele . Fano congruences of index 3 and alternating 3-forms. Annales de l'Institut Fourier. 2017, 67(5), 2099-2165 | |
dc.identifier.uri | http://hdl.handle.net/10852/59368 | |
dc.description.abstract | We study congruences of lines Xω defined by a sufficiently general choice of an alternating 3-form ω in n dimensions, as Fano manifolds of index 3 and dimension n-1. These congruences include the G2-variety for n=6 and the variety of reductions of projected ℙ 2 ×ℙ 2 for n=7.
We compute the degree of X ω as the n-th Fine number and study the Hilbert scheme of these congruences proving that the choice of ω bijectively corresponds to X ω except when n=5. The fundamental locus of the congruence is also studied together with its singular locus: these varieties include the Coble cubic for n=8 and the Peskine variety for n=9.
The residual congruence Y of X ω with respect to a general linear congruence containing X ω is analysed in terms of the quadrics containing the linear span of X ω . We prove that Y is Cohen–Macaulay but non-Gorenstein in codimension 4. We also examine the fundamental locus G of Y of which we determine the singularities and the irreducible components. | en_US |
dc.language | EN | |
dc.publisher | Institut Fourier | |
dc.rights | Attribution - Pas de Modification 3.0 France | |
dc.rights.uri | https://creativecommons.org/licenses/by-nd/3.0/fr/ | |
dc.title | Fano congruences of index 3 and alternating 3-forms | en_US |
dc.type | Journal article | en_US |
dc.creator.author | Ranestad, Kristian | |
dc.creator.author | Mezzetti, Emilia | |
dc.creator.author | De Poi, Pietro | |
dc.creator.author | Faenzi, Daniele | |
cristin.unitcode | 185,15,13,0 | |
cristin.unitname | Matematisk institutt | |
cristin.ispublished | true | |
cristin.fulltext | original | |
cristin.qualitycode | 2 | |
dc.identifier.cristin | 1378290 | |
dc.identifier.bibliographiccitation | info:ofi/fmt:kev:mtx:ctx&ctx_ver=Z39.88-2004&rft_val_fmt=info:ofi/fmt:kev:mtx:journal&rft.jtitle=Annales de l'Institut Fourier&rft.volume=67&rft.spage=2099&rft.date=2017 | |
dc.identifier.jtitle | Annales de l'Institut Fourier | |
dc.identifier.volume | 67 | |
dc.identifier.issue | 5 | |
dc.identifier.startpage | 2099 | |
dc.identifier.endpage | 2165 | |
dc.identifier.doi | 10.5802/aif.3131 | |
dc.identifier.urn | URN:NBN:no-62054 | |
dc.type.document | Tidsskriftartikkel | en_US |
dc.type.peerreviewed | Peer reviewed | |
dc.source.issn | 0373-0956 | |
dc.identifier.fulltext | Fulltext https://www.duo.uio.no/bitstream/handle/10852/59368/2/AIF_2017__67_5_2099_0.pdf | |
dc.type.version | PublishedVersion | |
dc.relation.project | NFR/239015 | |