Leiden University Student Repository

Karl, Tim (2025)

The maximum number of lines on a smooth quartic surface

Master thesis | Mathematics (MSc)

In this thesis, we take a close look at a theorem from Rams and Schütt [20] which states that a smooth quartic surface in 3-dimensional projective space over an algebraically closed field of characteristic not equal to 2 or 3 contains at most 64 lines. In Chapter 1, we cover the well-known theorem that smooth cubic surfaces contain exactly 27 lines. In Chapter 2, we present a basic introduction into elliptic curves and elliptic surfaces. In Chapter 3, we follow Rams’ and Schütt’s proof to show the aforementioned theorem while providing additional details and presenting computations that they omitted. We improve on one of the intermediate results in [20] and show that if two inflectious lines on a smooth quartic surface intersect, the surface is projectively equivalent to the Schur quartic.

Author

Karl, Tim

Faculty

Faculty of Science

Specialisation

Science Communication & Society

Supervisors

Luijk, R.M. van

ECTS Credits

23

Language

en