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Waring rank of binary forms, harmonic cross-ratio and golden ratio

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.

preprint2020arXivOpen access
Alexandru DimcaGabriel Sticlaru
math.AG
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Open access2 authors1 topic
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Alexandru DimcaGabriel Sticlaru

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