Counting Lines on Quartic Surfaces

We prove the sharp bound of at most 64 lines on projective quartic surfacesS⊂ ℙ3(ℂ) (resp. affine quarticsS⊂ ℂ3) that are not ruled by lines. We study configurations of lines on certain non-K3 surfaces of degree four and give various examples of singular quartics with many lines. 2010Mathematics Sub...

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Veröffentlicht in:Taiwanese journal of mathematics 2016-08, Vol.20 (4), p.769-785
Hauptverfasser: González-Alonso, Víctor, Rams, Sławomir
Format: Artikel
Sprache:eng
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Zusammenfassung:We prove the sharp bound of at most 64 lines on projective quartic surfacesS⊂ ℙ3(ℂ) (resp. affine quarticsS⊂ ℂ3) that are not ruled by lines. We study configurations of lines on certain non-K3 surfaces of degree four and give various examples of singular quartics with many lines. 2010Mathematics Subject Classification.Primary: 14J25, 14N25; Secondary: 14N20, 14J70. Key words and phrases.Line, Quartic surface, Non-ADE singularity.
ISSN:1027-5487
2224-6851
DOI:10.11650/tjm.20.2016.7135