We prove a theorem which implies that all Segre-Veronese varieties of multidegree (d1, . . . , dk) and format (n1, . . . , nk) with n1 ≥ · · · ≥ nk > 0 are not defective if d1 ≥ 3, d2 ≥ 3 and di ≥ 2 for all i > 2. As a particular case we prove the non-defectivity of any Segre-Veronese variety with at least 2 factors and di ≥ 3 for all i, extending to the case k > 2 a theorem of Galuppi and Oneto. Our general result also shows that many Segre-Veronese varieties with 2 factors are not secant defective if they are embedded in bidegree (x, 2), x ≥ 4.

On the non-defectivity of Segre-Veronese embeddings / Ballico, Edoardo. - In: MATHEMATISCHE ZEITSCHRIFT. - ISSN 0025-5874. - STAMPA. - 2024, 308:1(2024), pp. 601-615. [10.1007/s00209-024-03573-x]

On the non-defectivity of Segre-Veronese embeddings

Ballico, Edoardo
2024-01-01

Abstract

We prove a theorem which implies that all Segre-Veronese varieties of multidegree (d1, . . . , dk) and format (n1, . . . , nk) with n1 ≥ · · · ≥ nk > 0 are not defective if d1 ≥ 3, d2 ≥ 3 and di ≥ 2 for all i > 2. As a particular case we prove the non-defectivity of any Segre-Veronese variety with at least 2 factors and di ≥ 3 for all i, extending to the case k > 2 a theorem of Galuppi and Oneto. Our general result also shows that many Segre-Veronese varieties with 2 factors are not secant defective if they are embedded in bidegree (x, 2), x ≥ 4.
2024
1
Ballico, Edoardo
On the non-defectivity of Segre-Veronese embeddings / Ballico, Edoardo. - In: MATHEMATISCHE ZEITSCHRIFT. - ISSN 0025-5874. - STAMPA. - 2024, 308:1(2024), pp. 601-615. [10.1007/s00209-024-03573-x]
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/11572/423130
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