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We consider generic degenerate subvarieties . We determine an integer , depending on the varieties, and for we compute dimension and degree formulas for the Hadamard product of the varieties . Moreover, if the varieties are smooth, their Hadamard product is smooth too. For , if the are generically -parameterized, the dimension and degree formulas still hold. However, the Hadamard product can be singular and we give a lower bound for the dimension of the singular locus.
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Gabriele Calussi, Enrico Carlini, Giuliana Fatabbi, Anna Lorenzini, On the Hadamard product of degenerate subvarieties. Port. Math. 76 (2019), no. 2, pp. 123–141DOI 10.4171/PM/2029