On quartics with lines of the second kind
Slawomir Rams, Matthias Schuett
TL;DR
This paper investigates the geometric properties of quartic surfaces in projective three-space containing a special type of line, correcting historical inaccuracies in the classical literature for algebraically closed fields of characteristic not 2 or 3.
Contribution
It provides a detailed analysis of quartic surfaces with lines of the second kind and rectifies Segre's 1943 claims in the complex case.
Findings
Clarified the geometry of quartic surfaces with lines of the second kind
Corrected Segre's historical assertions for the complex case
Enhanced understanding of quartic surface configurations
Abstract
We study the geometry of quartic surfaces in IP^3 that contain a line of the second kind over algebraically closed fields of characteristic different from 2,3. In particular, we correct Segre's claims made for the complex case in 1943.
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