Tohoku Mathematical Journal
2022

September
SECOND SERIES VOL. 74, NO. 3

Tohoku Math. J.
74 (2022), 489-499

Title WARING RANK OF BINARY FORMS, HARMONIC CROSS-RATIO AND GOLDEN RATIO

Author Alexandru Dimca and Gabriel Sticlaru

(Received October 21, 2020, revised May 20, 2021)
Abstract. We discuss the Waring rank of binary forms of degree 4 and 5, without multiple factors, and point out unexpected relations to the harmonic cross-ratio, j-invariants and the golden ratio. These computations of ranks for binary forms are used to show that the combinatorics of a line arrangement in the complex projective plane does not determine the Waring rank of the defining equation even in very simple situations.

Mathematics Subject Classification. Primary 14J70; Secondary 14B05, 32S05, 32S22.

Key words and phrases. Waring decomposition, Waring rank, line arrangement, cross-ratio, golden ratio.

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