Mathematics – Algebraic Geometry
Scientific paper
2009-03-16
Journ. of P. and A. Algebra, 215, (2011), pp. 201-220
Mathematics
Algebraic Geometry
30 pages
Scientific paper
10.1016/j.jpaa.2010.04.008
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 Pl\"ucker space, then 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.
Arrondo Enrique
Bernardi Alessandra
No associations
LandOfFree
On the variety parametrizing completely decomposable polynomials does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.
If you have personal experience with On the variety parametrizing completely decomposable polynomials, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and On the variety parametrizing completely decomposable polynomials will most certainly appreciate the feedback.
Profile ID: LFWR-SCP-O-223961