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.File | Dimensione | Formato | |
---|---|---|---|
rtimesp3.pdf
embargo fino al 27/07/2025
Tipologia:
Post-print referato (Refereed author’s manuscript)
Licenza:
Tutti i diritti riservati (All rights reserved)
Dimensione
343.76 kB
Formato
Adobe PDF
|
343.76 kB | Adobe PDF | Visualizza/Apri |
s00209-024-03573-x.pdf
Solo gestori archivio
Tipologia:
Versione editoriale (Publisher’s layout)
Licenza:
Tutti i diritti riservati (All rights reserved)
Dimensione
392.23 kB
Formato
Adobe PDF
|
392.23 kB | Adobe PDF | Visualizza/Apri |
I documenti in IRIS sono protetti da copyright e tutti i diritti sono riservati, salvo diversa indicazione