Let $X^{(n,m)}_{(1,d)}$ denote the Segre-Veronese embedding of $mathbb{P}^n imes mathbb{P}^m$ via the sections of the sheaf $mathcal{O}(1,d)$. We study the dimensions of higher secant varieties of $X^{(n,m)}_{(1,d)}$ and we prove that there is no defective $s^{th}$ secant variety, except possibly for $n$ values of $s$. Moreover when ${m+d choose d}$ is multiple of $(m+n+1)$, the $s^{th}$ secant variety of $X^{(n,m)}_{(1,d)}$ has the expected dimension for every $s$.

Higher secant varieties of Pn×Pm embedded in bi-degree (1,d) / Bernardi, Alessandra; Enrico, Carlini; Maria Virginia, Catalisano. - In: JOURNAL OF PURE AND APPLIED ALGEBRA. - ISSN 0022-4049. - 215:(2011), pp. 2853-2858. [10.1016/j.jpaa.2011.04.005]

Higher secant varieties of Pn×Pm embedded in bi-degree (1,d)

Bernardi, Alessandra;
2011-01-01

Abstract

Let $X^{(n,m)}_{(1,d)}$ denote the Segre-Veronese embedding of $mathbb{P}^n imes mathbb{P}^m$ via the sections of the sheaf $mathcal{O}(1,d)$. We study the dimensions of higher secant varieties of $X^{(n,m)}_{(1,d)}$ and we prove that there is no defective $s^{th}$ secant variety, except possibly for $n$ values of $s$. Moreover when ${m+d choose d}$ is multiple of $(m+n+1)$, the $s^{th}$ secant variety of $X^{(n,m)}_{(1,d)}$ has the expected dimension for every $s$.
2011
Bernardi, Alessandra; Enrico, Carlini; Maria Virginia, Catalisano
Higher secant varieties of Pn×Pm embedded in bi-degree (1,d) / Bernardi, Alessandra; Enrico, Carlini; Maria Virginia, Catalisano. - In: JOURNAL OF PURE AND APPLIED ALGEBRA. - ISSN 0022-4049. - 215:(2011), pp. 2853-2858. [10.1016/j.jpaa.2011.04.005]
File in questo prodotto:
Non ci sono file associati a questo prodotto.

I documenti in IRIS sono protetti da copyright e tutti i diritti sono riservati, salvo diversa indicazione

Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/11572/134867
Citazioni
  • ???jsp.display-item.citation.pmc??? ND
  • Scopus 14
  • ???jsp.display-item.citation.isi??? 12
social impact