The paper is devoted to a detailed study of sextics in three variables having a decomposition as a sum of nine powers of linear forms. This is indeed the unique case of a Veronese image X of the plane which, in the terminology introduced by Ciliberto and the first author, is {\it weakly defective}, and non-identifiable: a general sextic of the 9-secant variety of X has two minimal decompositions.
Chiantini, L., Ottaviani, G. (2023). A footnote to a footnote to a paper of B. Segre. In F.F. Thomas Dedieu (a cura di), The art of doing algebraic geometry (pp. 93-117). Berlin : Springer [10.1007/978-3-031-11938-5_4].
A footnote to a footnote to a paper of B. Segre
Luca Chiantini;
2023-01-01
Abstract
The paper is devoted to a detailed study of sextics in three variables having a decomposition as a sum of nine powers of linear forms. This is indeed the unique case of a Veronese image X of the plane which, in the terminology introduced by Ciliberto and the first author, is {\it weakly defective}, and non-identifiable: a general sextic of the 9-secant variety of X has two minimal decompositions.
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Utilizza questo identificativo per citare o creare un link a questo documento:
https://hdl.handle.net/11365/1233107