We consider generic degenerate subvarieties Xi ⊂ Pn. We determine an integer N, depending on the varieties, and for n≥N we compute dimension and degree formulas for the Hadamard product of the varieties Xi. Moreover, if the varieties Xi are smooth, their Hadamard product is smooth too. For n < N, if the Xi are generically di-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.
On the Hadamard product of degenerate subvarieties
G. Calussi;G. Fatabbi;A. Lorenzini
2019
Abstract
We consider generic degenerate subvarieties Xi ⊂ Pn. We determine an integer N, depending on the varieties, and for n≥N we compute dimension and degree formulas for the Hadamard product of the varieties Xi. Moreover, if the varieties Xi are smooth, their Hadamard product is smooth too. For n < N, if the Xi are generically di-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.File in questo prodotto:
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