A Partial Stratification of Secant Varieties of Veronese Varieties via Curvilinear Subschemes
نویسندگان
چکیده
We give a partial “quasi-stratification” of the secant varieties of the order d Veronese variety Xm,d of P. It covers the set σt(Xm,d) † of all points lying on the linear span of curvilinear subschemes of Xm,d, but two “quasi-strata” may overlap. For low border rank two different “quasi-strata” are disjoint and we compute the symmetric rank of their elements. Our tool is the Hilbert schemes of curvilinear subschemes of Veronese varieties. To get a stratification we attach to each P ∈ σt(Xm,d) the minimal label of a quasi-stratum containing it.
منابع مشابه
Tensor Ranks on Tangent Developable of Segre Varieties
We describe the stratification by tensor rank of the points belonging to the tangent developable of any Segre variety. We give algorithms to compute the rank and a decomposition of a tensor belonging to the secant variety of lines of any Segre variety. We prove Comon’s conjecture on the rank of symmetric tensors for those tensors belonging to tangential varieties to Veronese varieties.
متن کاملOn the stratification of secant varieties of Veronese varieties via symmetric rank
When considering σr(X), the variety of r-secant P r−1 to a projective variety X, one question which arises is what are the possible values of the X-rank of points on σr(X), apart from the generic value r? This geometric problem is of particular relevance (also for Applied Math) when X is a variety parameterizing some kind of tensors. We study here the case when X is a Veronese variety (i.e. the...
متن کاملNew Examples of Defective Secant Varieties of Segre-veronese Varieties
We prove the existence of defective secant varieties of three-factor and four-factor Segre-Veronese varieties embedded in certain multi-degree. These defective secant varieties were previously unknown and are of importance in the classification of defective secant varieties of Segre-Veronese varieties with three or more factors.
متن کاملSecant Varieties of Segre-veronese Varieties
In this paper we study the dimension of secant varieties of Segre-Veronese varieties P × P embedded by the morphism given by O(1, 2). Given the dimensions m, n, we provide two functions s(m, n) and s(m, n), such that the s secant variety is nondefective, i.e. it has the expected dimension, if s ≤ s(m, n) or s ≥ s(m, n). Finally, we present a conjecturally complete list of defective secant varie...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
عنوان ژورنال:
دوره شماره
صفحات -
تاریخ انتشار 2012