Archivio Istituzionale della RicercaWe 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 / Calussi, G.; Carlini, E.; Fatabbi, G.; Lorenzini, A.. - In: PORTUGALIAE MATHEMATICA. - ISSN 0032-5155. - STAMPA. - 76:2(2019), pp. 123-141. [10.4171/PM/2029]
On the hadamard product of degenerate subvarieties
Carlini E.;
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.
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OnTheHadaamrdProductOfDegenerateSub.pdf
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https://hdl.handle.net/11583/2832872