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On the variety parameterizing completely decomposable polynomials

Arrondo Esteban, Enrique and Bernadi, Alessandra (2011) On the variety parameterizing completely decomposable polynomials. Journal of pure and applied algebra, 215 (3). pp. 201-220. ISSN 0022-4049

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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)(P(n)), with the Grassmannian of (n - 1)-dimensional projective subspaces of P(n+d-1). We compute the dimension of some secant varieties to Split(d)(P(n)). Moreover by using an invariant embedding of the Veronese variety into the Plucker space, we are able to compute the intersection of G(n - 1, n + d - 1) with Split(d)(P(n)), some of its secant varieties, the tangential variety and the second osculating space to the Veronese variety.


Item Type:Article
Uncontrolled Keywords:Secant varieties; Grassmann varieties
Subjects:Sciences > Mathematics > Differential geometry
Sciences > Mathematics > Algebra
ID Code:14739
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