Restricted secant varieties of Grassmannians
نویسندگان
چکیده
Restricted secant varieties of Grassmannians are constructed from sums points corresponding to $k$-planes with the restriction that their intersection has a prescribed dimension. We study dimensions restricted and relate them analogous question for secants via an incidence variety construction. define notion expected dimension give formula all holds if Baur-Draisma-deGraaf Conjecture on non-defectivity is true. also demonstrate example calculations in Macaulay2, point out ways make these more efficient. show potential application coding theory.
منابع مشابه
Grassmannians of Secant Varieties
For an irreducible projective variety X, we study the family of h-planes contained in the secant variety Sec k (X), for 0 < h < k. These families have an expected dimension and we study varieties for which the expected dimension is not attained; for these varieties, making general consecutive projections to lower dimensional spaces, we do not get the expected singularities. In particular, we ex...
متن کاملSecant Varieties of Toric Varieties
If X is a smooth projective toric variety of dimension n we give explicit conditions on characters of the torus giving an embedding X →֒ Pr that guarantee dimSecX = 2n+ 1. We also give necessary and sufficient conditions for a general point of SecX to lie on a unique secant line when X is embedded into Pr using a complete linear system. For X of dimension 2 and 3 we give formulas for deg SecX in...
متن کاملSecant varieties
The goal of this talk is to introduce secant varieies and show connections of secant varieties of Veronese variety to the Waring problem. 1 Secant varieties Let X ⊂ P be a variety over k, where k is algebraically closed field of characteristic 0 (or just assume k = C). Definition 1.1. For s ≥ 1 the s-th higher secant variety of X is
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 کاملEquations for secant varieties of Chow varieties
The Chow variety of polynomials that decompose as a product of linear forms has been studied for more than 100 years. Finding equations in the ideal of secant varieties of Chow varieties would enable one to measure the complexity the permanent polynomial. In this article, I use the method of prolongation to obtain equations for secant varieties of Chow varieties as GL(V )-modules.
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
ژورنال
عنوان ژورنال: Collectanea Mathematica
سال: 2023
ISSN: ['2038-4815', '0010-0757']
DOI: https://doi.org/10.1007/s13348-023-00399-4