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This paper explores the dimensions of higher secant varieties to Segre-Veronese varieties. The main goal of this paper is to introduce two different inductive techniques. These techniques enable one to reduce the computation of the dimension of the secant variety in a high-dimensional case to the computation of the dimensions of secant varieties in low-dimensional cases. As an application of these inductive approaches, we will prove non-defectivity of secant varieties of certain two-factor Segre-Veronese varieties. We also use these methods to give a complete classification of defective sth Segre–Veronese varieties for small s. In the final section, we propose a conjecture about defective two-factor Segre–Veronese varieties. 相似文献
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In this paper we study the k-th osculating variety of the order d Veronese embedding of P
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. In particular, for k=n=2 we show that the corresponding secant varieties have the expected dimension except in one case. 相似文献
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The sphericality of tangential varieties of rational homogeneousvarieties is determined. The homogeneous coordinate rings andrings of covariants of the tangential varieties of homogenouslyembedded compact Hermitian symmetric spaces (CHSS) are determined.Bounds on the degrees of generators of the ideals of tangentialvarieties of CHSS are given, and more explicit information isobtained about the ideals in certain cases. 相似文献
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We find minimal generators for the ideals of secant varietiesof Segre varieties in the cases of k(1 x n x m) for all k, n,m, 2(n x m x p x r) for all n, m, p, r (GSS conjecture for fourfactors), and 3(n x m x p) for all n, m, p and prove they arenormal with rational singularities in the first case and arithmeticallyCohen–Macaulay in the second two cases. 相似文献
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Edoardo Ballico Claudio Fontanari Cristiano Bocci Enrico Carlini 《Rendiconti del Circolo Matematico di Palermo》2004,53(3):429-436
We generalize the classical Terracini’s Lemma to higher order osculating spaces to secant varieties. As an application, we
address with the so-called Horace method the case of thed-Veronese embedding of the projective 3-space.
This research is part of the T.A.S.C.A. project of I.N.d.A.M., supported by P.A.T. (Trento) and M.I.U.R. (Italy). 相似文献
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We show that the secant varieties of rank three compact Hermitian symmetric spaces in their minimal homogeneous embeddings are normal, with rational singularities. We show that their ideals are generated in degree three—with one exception, the secant variety of the 21-dimensional spinor variety in P63 where we show that the ideal is generated in degree four. We also discuss the coordinate rings of secant varieties of compact Hermitian symmetric spaces. 相似文献
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《Journal of Pure and Applied Algebra》2022,226(6):106969
We investigate the secant dimensions and the identifiability of flag varieties parametrizing flags of subspaces of a fixed vector space. We give numerical conditions ensuring that secant varieties of flag varieties have the expected dimension, and that a general point on these secant varieties is identifiable. 相似文献
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Gałązka Maciej Mańdziuk Tomasz Rupniewski Filip 《Foundations of Computational Mathematics》2023,23(4):1167-1214
Foundations of Computational Mathematics - Cactus varieties are a generalization of secant varieties. They are defined using linear spans of arbitrary finite schemes of bounded length, while secant... 相似文献
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E. Ballico 《Rendiconti del Circolo Matematico di Palermo》1921,45(1):93-104
Let π:X→Y be the blowing up of the projective varietyY at s general points. Here we study the higher order secant varieties of the linearly normal embeddings ofX andY into projective spaces. We give conditions on the embedding ofY which imply that the firstt secant varieties of a related embedding ofX have the expected dimension. 相似文献
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E. Ballico 《Rendiconti del Circolo Matematico di Palermo》1996,45(1):93-104
Let π:X→Y be the blowing up of the projective varietyY at s general points. Here we study the higher order secant varieties of the linearly normal embeddings ofX andY into projective spaces. We give conditions on the embedding ofY which imply that the firstt secant varieties of a related embedding ofX have the expected dimension. 相似文献
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Fulvio Gesmundo 《Annali dell'Universita di Ferrara》2013,59(2):285-302
This paper studies the defectivity of secant varieties of Segre varieties. We prove that there exists an asymptotic lower estimate for the greater non-defective secant variety (without filling the ambient space) of any given Segre variety. In particular, we prove that the ratio between the greater non-defective secant variety of a Segre variety and its expected rank is lower bounded by a value depending just on the number of factors of the Segre variety. Moreover, in the final section, we present some results obtained by explicit computation, proving the non-defectivity of all the secant varieties of Segre varieties of the shape $(\mathbb{P }^{n})^4$ , with $2 \le n\le 10$ , except at most $\sigma _{199}((\mathbb{P }^8)^4)$ and $\sigma _{357}((\mathbb{P }^{10})^4)$ . 相似文献
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E. Ballico 《Results in Mathematics》1997,32(1-2):29-36
Here we give the geometric foundations of the theory of joins and higher secant varieties. 相似文献
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New classes of modules of equations for secant varieties of Veronese varieties are defined using representation theory and geometry. Some old modules of equations (catalecticant minors) are revisited to determine when they are sufficient to give scheme-theoretic defining equations. An algorithm to decompose a general ternary quintic as the sum of seven fifth powers is given as an illustration of our methods. Our new equations and results about them are put into a larger context by introducing vector bundle techniques for finding equations of secant varieties in general. We include a few homogeneous examples of this method. 相似文献