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arXiv · 1608.04209

Lines on K3 quartic surfaces in characteristic 3

Davide Cesare Veniani
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Abstract

We investigate the number of straight lines contained in a K3 quartic surface \(X\) defined over an algebraically closed field of characteristic 3. We prove that if \(X\) contains 112 lines, then \(X\) is projectively equivalent to the Fermat quartic surface; otherwise, \(X\) contains at most 67 lines. We improve this bound to 58 if \(X\) contains a star (ie four distinct lines intersecting at a smooth point of \(X\)). Explicit equations of three 1-dimensional families of smooth quartic surfaces with 58 lines, and of a quartic surface with 8 singular points and 48 lines are provided.

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Davide Cesare Veniani. 2016-08-15. Lines on K3 quartic surfaces in characteristic 3. https://doi.org/10.1007/s00229-021-01284-9

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