Relevant bibliographies by topics / Rational Homogeneous variety

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  1. Journal articles
  2. Dissertations / Theses

Academic literature on the topic 'Rational Homogeneous variety'

Author: Grafiati
Published: 11 March 2023

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Journal articles on the topic "Rational Homogeneous variety"

1

Zhu, Yi. "HOMOGENEOUS SPACE FIBRATIONS OVER SURFACES." Journal of the Institute of Mathematics of Jussieu 18, no. 2 (April 3, 2017): 293–327. http://dx.doi.org/10.1017/s1474748017000081.

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By studying the theory of rational curves, we introduce a notion of rational simple connectedness for projective homogeneous spaces. As an application, we prove that over a function field of an algebraic surface over an algebraically closed field, a variety whose geometric generic fiber is a projective homogeneous space admits a rational point if and only if the elementary obstruction vanishes.
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Morishita, Masanori, and Takao Watanabe. "A note on the mean value theorem for special homogeneous spaces." Nagoya Mathematical Journal 143 (September 1996): 111–17. http://dx.doi.org/10.1017/s0027763000005948.

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Let G be a connected linear algebraic group and X an algebraic variety, both defined over Q, the field of rational numbers. Suppose that G acts on X transitively and the action is defined over Q. Suppose that the set of rational points X(Q) is non-empty. Choosing x ∈ X(Q) allows us to identify G/Gx and X as varieties over Q, there Gx is the stabilizer of x.
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Almeida, L. C. O., and S. C. Coutinho. "On Homogenous Minimal Involutive Varieties." LMS Journal of Computation and Mathematics 8 (2005): 301–15. http://dx.doi.org/10.1112/s1461157000001005.

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AbstractЅ(2n,k) be the variety of homogeneous polynomials of degree k in 2n variables. The authors of this paper give a computer-assisted proof that there is an analytic open set Ω of Ѕ(4,3) such that the surface F = 0 is a minimal homogeneous involutive variety of ℂ4 for all F ∈ Ω. As part of the proof, they give an explicit example of a polynomial with rational coefficients that belongs to Ω.
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Lee, Kyoung-Seog, and Kyeong-Dong Park. "Equivariant Ulrich bundles on exceptional homogeneous varieties." Advances in Geometry 21, no. 2 (April 1, 2021): 187–205. http://dx.doi.org/10.1515/advgeom-2020-0018.

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Abstract We prove that the only rational homogeneous varieties with Picard number 1 of the exceptional algebraic groups admitting irreducible equivariant Ulrich vector bundles are the Cayley plane E 6/P 1 and the E 7-adjoint variety E 7/P 1. From this result,we see that a general hyperplane section F 4/P 4 of the Cayley plane also has an equivariant but non-irreducible Ulrich bundle.
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Carrillo-Pacheco, Jesús, and Fausto Jarquín-Zárate. "A Family Of Low Density Matrices In Lagrangian–Grassmannian." Special Matrices 6, no. 1 (May 1, 2018): 237–48. http://dx.doi.org/10.1515/spma-2018-0019.

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Abstract The aim of this paper is twofold. First, we show a connection between the Lagrangian- Grassmannian variety geometry defined over a finite field with q elements and the q-ary Low-Density Parity- Check codes. Second, considering the Lagrangian-Grassmannian variety as a linear section of the Grassmannian variety, we prove that there is a unique linear homogeneous polynomials family, up to linear combination, such that annuls the set of its rational points.
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MOSSA, ROBERTO. "BALANCED METRICS ON HOMOGENEOUS VECTOR BUNDLES." International Journal of Geometric Methods in Modern Physics 08, no. 07 (November 2011): 1433–38. http://dx.doi.org/10.1142/s0219887811005841.

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Let E → M be a holomorphic vector bundle over a compact Kähler manifold (M, ω) and let E = E1 ⊕ ⋯ ⊕ Em → M be its decomposition into irreducible factors. Suppose that each Ej admits a ω-balanced metric in Donaldson–Wang terminology. In this paper we prove that E admits a unique ω-balanced metric if and only if [Formula: see text] for all j, k = 1,…, m, where rj denotes the rank of Ej and Nj = dim H0(M, Ej). We apply our result to the case of homogeneous vector bundles over a rational homogeneous variety (M, ω) and we show the existence and rigidity of balanced Kähler embedding from (M, ω) into Grassmannians.
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Huneke, Craig, and Matthew Miller. "A Note on the Multiplicity of Cohen-Macaulay Algebras with Pure Resolutions." Canadian Journal of Mathematics 37, no. 6 (December 1, 1985): 1149–62. http://dx.doi.org/10.4153/cjm-1985-062-4.

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Let R = k[X1, …, Xn] with k a field, and let I ⊂ R be a homogeneous ideal. The algebra R/I is said to have a pure resolution if its homogeneous minimal resolution has the formSome of the known examples of pure resolutions include the coordinate rings of: the tangent cone of a minimally elliptic singularity or a rational surface singularity [15], a variety defined by generic maximal Pfaffians [2], a variety defined by maximal minors of a generic matrix [3], a variety defined by the submaximal minors of a generic square matrix [6], and certain of the Segre-Veronese varieties [1].If I is in addition Cohen-Macaulay, then Herzog and Kühl have shown that the betti numbers bi are completely determined by the twists di.
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Müller, J. Steffen. "Explicit Kummer varieties of hyperelliptic Jacobian threefolds." LMS Journal of Computation and Mathematics 17, no. 1 (2014): 496–508. http://dx.doi.org/10.1112/s1461157014000126.

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AbstractWe explicitly construct the Kummer variety associated to the Jacobian of a hyperelliptic curve of genus 3 that is defined over a field of characteristic not equal to 2 and has a rational Weierstrass point defined over the same field. We also construct homogeneous quartic polynomials on the Kummer variety and show that they represent the duplication map using results of Stoll.Supplementary materials are available with this article.
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9

Alekseevsky, Dmitri V., Jan Gutt, Gianni Manno, and Giovanni Moreno. "Lowest degree invariant second-order PDEs over rational homogeneous contact manifolds." Communications in Contemporary Mathematics 21, no. 01 (January 28, 2019): 1750089. http://dx.doi.org/10.1142/s0219199717500894.

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For each simple Lie algebra [Formula: see text] (excluding, for trivial reasons, type [Formula: see text]), we find the lowest possible degree of an invariant second-order PDE over the adjoint variety in [Formula: see text], a homogeneous contact manifold. Here a PDE [Formula: see text] has degree [Formula: see text] if [Formula: see text] is a polynomial of degree [Formula: see text] in the minors of [Formula: see text], with coefficient functions of the contact coordinate [Formula: see text], [Formula: see text], [Formula: see text] (e.g., Monge–Ampère equations have degree 1). For [Formula: see text] of type [Formula: see text] or [Formula: see text], we show that this gives all invariant second-order PDEs. For [Formula: see text] of types [Formula: see text] and [Formula: see text], we provide an explicit formula for the lowest-degree invariant second-order PDEs. For [Formula: see text] of types [Formula: see text] and [Formula: see text], we prove uniqueness of the lowest-degree invariant second-order PDE; we also conjecture that uniqueness holds in type [Formula: see text].
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10

Chipalkatti, Jaydeep. "Apolar Schemes of Algebraic Forms." Canadian Journal of Mathematics 58, no. 3 (June 1, 2006): 476–91. http://dx.doi.org/10.4153/cjm-2006-020-3.

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AbstractThis is a note on the classical Waring's problem for algebraic forms. Fix integers (n, d, r, s), and let ∧ be a general r-dimensional subspace of degree d homogeneous polynomials in n+1 variables. Let denote the variety of s-sided polar polyhedra of ∧. We carry out a case-by-case study of the structure of for several specific values of (n, d, r, s). In the first batch of examples, is shown to be a rational variety. In the second batch, is a finite set of which we calculate the cardinality.
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Dissertations / Theses on the topic "Rational Homogeneous variety"

1

Staffolani, Reynaldo. "Schur apolarity and how to use it." Doctoral thesis, Università degli studi di Trento, 2022. https://hdl.handle.net/11572/330432.

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The aim of this thesis is to investigate the tensor decomposition of structured tensors related to SL(n)-irreducible representations. Structured tensors are multilinear objects satisfying specific symmetry relations and their decompositions are of great interest in the applications. In this thesis we look for the decompositions of tensors belonging to irreducible representations of SL(n) into sum of elementary objects associated to points of SL(n)-rational hoogeneous varieties. This family includes Veronese varieties (symmetric tensors), Grassmann varieties (skew-symmetric tensors), and flag varieties. A classic tool to study the decomposition of symmetric tensors is the apolarity theory, which dates back to Sylvester. An analogous skew-symmetric apolarity theory for skew-symmetric tensors have been developed only few years ago. In this thesis we describe a global apolarity theory called Schur apolarity theory, which is suitable for tensors belonging to any irreducible representation of SL(n). Examples, properties and applications of such apolarity are studied with details and original results both in algebra and geoemtry are provided.
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Liang, Yongqi. "Principe local-global pour les zéro-cycles." Phd thesis, Université Paris Sud - Paris XI, 2011. http://tel.archives-ouvertes.fr/tel-00630560.

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Dans cette thèse, nous nous intéressons à l'étude de l'arithmétique (le principe de Hasse, l'approximation faible, et l'obstruction de Brauer-Manin) des zéro-cycles sur les variétés algébriques définies sur des corps de nombres. Nous introduisons la notion de sous-ensemble hilbertien généralisé. En utilisant la méthode de fibration, nous démontrons que l'obstruction de Brauer-Manin est la seule au principe de Hasse et à l'approximation faible pour les zéro-cycles de degré 1; et établissons l'exactitude d'une suite de type global-local concernant les groupes de Chow des zéro-cycles, pour certaines variétés qui admettent une structure de fibration au-dessus d'une courbe lisse ou au-dessus de l'espace projectif, où les hypothèses arithmétiques sont posées seulement sur les fibres au-dessus d'un sous-ensemble hilbertien généralisé.De plus, nous relions l'arithmétique des points rationnels et l'arithmétique des zérocycles de degré 1 sur les variétés géométriquement rationnellement connexes. Comme application, nous trouvons que l'obstruction de Brauer-Manin est la seule au principe de Hasse et à l'approximation faible pour les zéro-cycles de degré 1 sur- les espaces homogènes d'un groupe algébrique linéaire à stabilisateur connexe,- certains fibrés en surfaces de Châtelet au-dessus d'une courbe lisse ou au-dessus de l'espace projectif (en particulier, les solides de Poonen).
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