Skip to Main content Skip to Navigation
Journal articles

Higher secant varieties of P^n × P^m embedded in bi-degree (1,d)

Alessandra Bernardi 1 Enrico Carlini 2 Maria Virgina Catalisano 3
1 GALAAD - Geometry, algebra, algorithms
CRISAM - Inria Sophia Antipolis - Méditerranée , UNS - Université Nice Sophia Antipolis (... - 2019), CNRS - Centre National de la Recherche Scientifique : UMR6621
Abstract : Let $X^{(n,m)}_{(1,d)}$ denote the Segre\/-Veronese embedding of $\PP n \times \PP m$ 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 a multiple of $(m+n+1)$, the $s^{th}$ secant variety of $X^{(n,m)}_{(1,d)}$ has the expected dimension for every $s$.
Document type :
Journal articles
Complete list of metadatas

Cited literature [27 references]  Display  Hide  Download

https://hal.inria.fr/hal-00645976
Contributor : Alessandra Bernardi <>
Submitted on : Monday, November 28, 2011 - 10:44:02 PM
Last modification on : Monday, October 12, 2020 - 10:27:38 AM
Long-term archiving on: : Wednesday, February 29, 2012 - 2:31:31 AM

File

BCC.pdf
Files produced by the author(s)

Identifiers

Collections

Citation

Alessandra Bernardi, Enrico Carlini, Maria Virgina Catalisano. Higher secant varieties of P^n × P^m embedded in bi-degree (1,d). Journal of Pure and Applied Algebra, Elsevier, 2011, 215 (12), pp.2853-2858. ⟨10.1016/j.jpaa.2011.04.005⟩. ⟨hal-00645976⟩

Share

Metrics

Record views

445

Files downloads

310