Generalized pencils of conics derived from cubics
dc.contributor.author
Halbeisen, Lorenz
dc.contributor.author
Hungerbühler, Norbert
dc.date.accessioned
2020-10-19T14:25:26Z
dc.date.available
2020-10-19T02:46:33Z
dc.date.available
2020-10-19T14:25:26Z
dc.date.issued
2020-12
dc.identifier.issn
0138-4821
dc.identifier.issn
2191-0383
dc.identifier.other
10.1007/s13366-020-00499-3
en_US
dc.identifier.uri
http://hdl.handle.net/20.500.11850/446471
dc.description.abstract
Given a cubic K. Then for each point P there is a conic CP associated to P. The conic CP is called the polar conic of K with respect to the pole P. We investigate the situation when two conics C0 and C1 are polar conics of K with respect to some poles P0 and P1, respectively. First we show that for any point Q on the line P0P1, the polar conic CQ of K with respect to Q belongs to the linear pencil of C0 and C1, and vice versa. Then we show that two given conics C0 and C1 can always be considered as polar conics of some cubic K with respect to some poles P0 and P1. Moreover, we show that P1 is determined by P0, but neither the cubic nor the point P0 is determined by the conics C0 and C1.
en_US
dc.language.iso
en
en_US
dc.publisher
Springer
en_US
dc.subject
Pencils
en_US
dc.subject
Conics
en_US
dc.subject
Polars
en_US
dc.subject
Polar conics of cubics
en_US
dc.title
Generalized pencils of conics derived from cubics
en_US
dc.type
Journal Article
dc.date.published
2020-04-15
ethz.journal.title
Beiträge zur Algebra und Geometrie = Contributions to algebra and geometry
ethz.journal.volume
61
en_US
ethz.journal.issue
4
en_US
ethz.journal.abbreviated
Beitr Algebra Geom
ethz.pages.start
681
en_US
ethz.pages.end
693
en_US
ethz.identifier.wos
ethz.identifier.scopus
ethz.publication.place
Heidelberg
en_US
ethz.publication.status
published
en_US
ethz.leitzahl
ETH Zürich::00002 - ETH Zürich::00012 - Lehre und Forschung::00007 - Departemente::02000 - Dep. Mathematik / Dep. of Mathematics::02003 - Mathematik Selbständige Professuren::03874 - Hungerbühler, Norbert / Hungerbühler, Norbert
ethz.leitzahl.certified
ETH Zürich::00002 - ETH Zürich::00012 - Lehre und Forschung::00007 - Departemente::02000 - Dep. Mathematik / Dep. of Mathematics::02003 - Mathematik Selbständige Professuren::03874 - Hungerbühler, Norbert / Hungerbühler, Norbert
ethz.date.deposited
2020-10-19T02:46:38Z
ethz.source
SCOPUS
ethz.eth
yes
en_US
ethz.availability
Metadata only
en_US
ethz.rosetta.installDate
2020-10-19T14:25:37Z
ethz.rosetta.lastUpdated
2023-02-06T20:35:31Z
ethz.rosetta.versionExported
true
ethz.COinS
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Journal Article [120835]