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Nets of conics and associated Artinian algebras of length 7
University of Borås, Faculty of Textiles, Engineering and Business.ORCID iD: 0000-0002-8001-6787
Paris, France.
Department of Mathematics, Northeastern University, Boston, MA, 02115, USA.ORCID iD: 0000-0002-1715-2786
2023 (English)In: European Journal of Mathematics, ISSN 2199-675X, E-ISSN 2199-6768, Vol. 9, no 2, article id 22Article in journal (Refereed) Published
Abstract [en]

We classify the orbits of nets of conics under the action of the projective linear group and we determine the specializations of these orbits, using geometric and algebraic methods. We study related geometric questions, as the parametrization of planar cubics. We show that Artinian algebras of Hilbert function H=(1,3,3,0) determined by nets, can be smoothed—deformed to a direct sum of fields; and that algebras of Hilbert function H=(1,r,2,0), determined by pencils of quadrics, can also be smoothed. This portion is a translation and update of a 1977 version, a typescript by the second two authors that was distributed as a preprint of University of Paris VII. In a new Historical Appendix A we describe related work prior to 1977. In an Update Appendix B we survey some developments since 1977 concerning nets of conics, related geometry, and deformations of Artinian algebras of small length.

Place, publisher, year, edition, pages
2023. Vol. 9, no 2, article id 22
National Category
Geometry
Identifiers
URN: urn:nbn:se:hb:diva-29575DOI: 10.1007/s40879-023-00600-9ISI: 000959966000001Scopus ID: 2-s2.0-85150776591OAI: oai:DiVA.org:hb-29575DiVA, id: diva2:1746462
Available from: 2023-03-28 Created: 2023-03-28 Last updated: 2024-02-01Bibliographically approved

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Abdallah, Nancy

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