Abstract
We determine the Waring ranks of all sextic binary forms with complex coefficients using a Geometric Invariant Theory approach. Using the five basic invariants for sextic binary forms, our results give a rapid method to determine the Waring rank of any given sextic binary form. In particular, we shed new light on a claim by E. B. Elliott at the end of the nineteenth century concerning the binary sextics with Waring rank 3. We show that for binary forms of arbitrary degree the cactus rank, a.k.a. scheme rank, is determined by the corresponding Waring rank. Finally, we determine the border ranks of all binary sextics.
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This work has been partially supported by the Romanian Ministry of Research and Innovation, CNCS - UEFISCDI, grant PN-III-P4-ID-PCE-2020-0029, within PNCDI III.
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Dimca, A., Sticlaru, G. Waring Ranks of Sextic Binary Forms via Geometric Invariant Theory. Transformation Groups (2022). https://doi.org/10.1007/s00031-022-09774-0
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DOI: https://doi.org/10.1007/s00031-022-09774-0