112 lines on smooth quartic surfaces (characteristic 3)

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.

11 pages; v2: minor edits following referee's comments

References in corpus (4)

• 64 lines on smooth quartic surfaces
• Genus 1 fibrations on the supersingular K3 surface in characteristic 2 with Artin invariant 1
• Elliptic Fibrations on Supersingular K3 Surface with Artin Invariant 1 in characteristic 3
• A bound for the number of lines lying on a nonsingular surface in $3$-space over a finite field

Cited by in corpus (13)

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• Counting Lines on Quartic Surfaces
• Smooth models of singular $K3$-surfaces
• At most 64 lines on smooth quartic surfaces (characteristic 2)
• The maximum number of lines lying on a K3 quartic surface
• Counting lines on surfaces, especially quintics
• Lines on K3 quartic surfaces in characteristic 2
• 24 rational curves on K3 surfaces
• Lines on K3 quartic surfaces in characteristic 3
• On a smooth quartic surface containing 56 lines which is isomorphic as a K3 surface to the Fermat quartic
• Lines on K3-quartics via triangular sets
• Conics on Barth--Bauer octics
• Counting Lines with Vinberg's algorithm