Taiwanese Journal of Mathematics

Counting Lines on Quartic Surfaces

Víctor González-Alonso and Sławomir Rams

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We prove the sharp bound of at most $64$ lines on projective quartic surfaces $S \subset \mathbb{P}^3(\mathbb{C})$ (resp. affine quartics $S \subset \mathbb{C}^3$) 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.

Article information

Taiwanese J. Math., Volume 20, Number 4 (2016), 769-785.

First available in Project Euclid: 1 July 2017

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Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier

Primary: 14J25: Special surfaces {For Hilbert modular surfaces, see 14G35} 14N25: Varieties of low degree
Secondary: 14N20: Configurations and arrangements of linear subspaces 14J70: Hypersurfaces

line quartic surface non-ADE singularity


González-Alonso, Víctor; Rams, Sławomir. Counting Lines on Quartic Surfaces. Taiwanese J. Math. 20 (2016), no. 4, 769--785. doi:10.11650/tjm.20.2016.7135. https://projecteuclid.org/euclid.twjm/1498874490

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