Hadamard non-defectivity conjecture for secant varieties of Segre-Veronese varieties

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Let SVd,nSV_{\mathbf{d},\mathbf{n}} be a Segre-Veronese variety, let σr(SVd,n)\sigma_{\mathbf{r}}(SV_{\mathbf{d},\mathbf{n}}) denote its secant variety, and let a Hadamard product mean the coordinatewise product of such varieties. Hadamard non-defectivity conjecture. For any d\mathbf{d} and any n\mathbf{n}, Hadamard products of secant varieties of Segre-Veronese varieties σr(SVd,n)\sigma_{\mathbf{r}}(SV_{\mathbf{d},\mathbf{n}}) are not Hadamard-defective. This conjecture is motivated by computational verification in several defective families, but the general assertion remains open and would provide a direct non-defectivity statement beyond the cases currently accessible by the dimension bounds.

References

Primary source

Dario Antolini, Guido Montúfar and Alessandro Oneto, “Hadamard ranks of algebraic varieties”, arXiv:2510.05231 (2025).

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