Skip to Main content Skip to Navigation
New interface
Journal articles

On the variety parameterizing completely decomposable polynomials

Enrique Arrondo 1 Alessandra Bernardi 2 
2 GALAAD - Geometry, algebra, algorithms
CRISAM - Inria Sophia Antipolis - Méditerranée , UNS - Université Nice Sophia Antipolis (1965 - 2019), CNRS - Centre National de la Recherche Scientifique : UMR6621
Abstract : The purpose of this paper is to relate the variety parameterizing completely decomposable homogeneous polynomials of degree $d$ in $n+1$ variables on an algebraically closed field, called $\Split_{d}(\PP n)$, with the Grassmannian of $n-1$ dimensional projective subspaces of $\PP {n+d-1}$. We compute the dimension of some secant varieties to $\Split_{d}(\PP n)$ and find a counterexample to a conjecture that wanted its dimension related to the one of the secant variety to $\GG (n-1, n+d-1)$. Moreover by using an invariant embedding of the Veronse variety into the Plücker space, we are able to compute the intersection of $\GG (n-1, n+d-1)$ with $\Split_{d}(\PP n)$, some of its secant variety, the tangential variety and the second osculating space to the Veronese variety.
Document type :
Journal articles
Complete list of metadata

Cited literature [19 references]  Display  Hide  Download
Contributor : Alessandra Bernardi Connect in order to contact the contributor
Submitted on : Monday, November 28, 2011 - 10:28:10 PM
Last modification on : Wednesday, September 14, 2022 - 5:14:26 PM
Long-term archiving on: : Friday, November 16, 2012 - 12:20:57 PM


Files produced by the author(s)




Enrique Arrondo, Alessandra Bernardi. On the variety parameterizing completely decomposable polynomials. Journal of Pure and Applied Algebra, 2011, 215 (3), pp.201-220. ⟨10.1016/j.jpaa.2010.04.008⟩. ⟨hal-00645963⟩



Record views


Files downloads