On the variety parametrizing completely decomposable polynomials.

Arrondo, Enrique ; Bernardi, Alessandra (2009) On the variety parametrizing completely decomposable polynomials. [Preprint]
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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.

Document type
Arrondo, Enrique
Bernardi, Alessandra
Decomposable polynomials, Secant varieties, Grassmannians, Veronese varieties
Deposit date
16 Mar 2009
Last modified
16 May 2011 12:10

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