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arXiv · 1409.7485

112 lines on smooth quartic surfaces (characteristic 3)

Slawomir Rams·Matthias Schuett
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Abstract

Over a field k of characteristic 3, we prove that there are no smooth quartic surfaces S in IP^3 with more than 112 lines. Moreover, the surface with 112 lines is projectively equivalent over k-bar to the Fermat quartic. As a key ingredient, we derive a characteristic free upper bound for the number of lines met by a quadric on a smooth quartic surface.

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Slawomir Rams, Matthias Schuett. 2014-09-26. 112 lines on smooth quartic surfaces (characteristic 3). https://doi.org/10.1093/qmath/hav018

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