Counting lines on surfaces, especially quintics

Abstract

We introduce certain rational functions on a smooth projective surface X in IP^3 which facilitate counting the lines on X. We apply this to smooth quintics in characteristic zero to prove that they contain no more than 127 lines, and that any given line meets at most 28 others. We construct examples which demonstrate that the latter bound is sharp.

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

References in corpus (1)

• Lines in supersingular quartics

Cited by in corpus (4)

• Conics in sextic $K3$-surfaces in ${\mathbb{P}}^4$
• Conics in Kummer quartics
• Counting Lines with Vinberg's algorithm
• Secant indices of projective varieties