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Waring problems and the Lefschetz properties

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Abstract

We study three variations of the Waring problem for homogeneous polynomials, concerning the Waring rank, the border rank and the cactus rank of a form. We show how the Lefschetz properties of the associated algebra affect them. We construct new families of wild forms, that is, forms whose cactus rank, of schematic nature, is bigger than the border rank, defined geometrically.

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Acknowledgements

The authors would like to thank the anonymous referee for the careful review of the article and for the suggestions that improved the article. We wish to thank F. Russo, A. Massarenti, I. Vainsencher for their insightful suggestions and conversations on the subject. A CNPq Research Fellowship partially supported the second named author (Proc. 309094/2020-8).

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  1. Universidade Federal Rural de Pernambuco, Av. Don Manoel de Medeiros s/n, Dois Irmãos, Recife, PE, 52171-900, Brazil

    Thiago Dias & Rodrigo Gondim

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  1. Thiago Dias
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  2. Rodrigo Gondim
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Dias, T., Gondim, R. Waring problems and the Lefschetz properties. Sel. Math. New Ser. 29, 32 (2023). https://doi.org/10.1007/s00029-023-00840-3

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