Relevant bibliographies by topics / Symmetric varieties

Contents

  1. Journal articles
  2. Dissertations / Theses
  3. Books
  4. Book chapters
  5. Conference papers

Academic literature on the topic 'Symmetric varieties'

Author: Grafiati
Published: 5 April 2025

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Journal articles on the topic "Symmetric varieties"

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Bifet, Emili. "On complete symmetric varieties." Advances in Mathematics 80, no. 2 (April 1990): 225–49. http://dx.doi.org/10.1016/0001-8708(90)90026-j.

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Guay, Nicolas. "Embeddings of symmetric varieties." Transformation Groups 6, no. 4 (December 2001): 333–52. http://dx.doi.org/10.1007/bf01237251.

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De Concini, C., and T. A. Springer. "Compactification of symmetric varieties." Transformation Groups 4, no. 2-3 (June 1999): 273–300. http://dx.doi.org/10.1007/bf01237359.

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Hong, Jiuzu, and Korkeat Korkeathikhun. "Nilpotent varieties in symmetric spaces and twisted affine Schubert varieties." Representation Theory of the American Mathematical Society 26, no. 20 (June 2, 2022): 585–615. http://dx.doi.org/10.1090/ert/613.

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We relate the geometry of Schubert varieties in twisted affine Grassmannian and the nilpotent varieties in symmetric spaces. This extends some results of Achar–Henderson in the twisted setting. We also get some applications to the geometry of the order 2 nilpotent varieties in certain classical symmetric spaces.
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Can, Mahir Bilen, Roger Howe, and Lex Renner. "Monoid embeddings of symmetric varieties." Colloquium Mathematicum 157, no. 1 (2019): 17–33. http://dx.doi.org/10.4064/cm7644-7-2018.

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Li, Yiqiang. "Quiver varieties and symmetric pairs." Representation Theory of the American Mathematical Society 23, no. 1 (January 17, 2019): 1–56. http://dx.doi.org/10.1090/ert/522.

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Uzawa, Tohru. "Symmetric varieties over arbitrary fields." Comptes Rendus de l'Académie des Sciences - Series I - Mathematics 333, no. 9 (November 2001): 833–38. http://dx.doi.org/10.1016/s0764-4442(01)02152-8.

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Cuntz, M., Y. Ren, and G. Trautmann. "Strongly symmetric smooth toric varieties." Kyoto Journal of Mathematics 52, no. 3 (2012): 597–620. http://dx.doi.org/10.1215/21562261-1625208.

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Pragacz, P. "Determinantal varieties and symmetric polynomials." Functional Analysis and Its Applications 21, no. 3 (July 1987): 249–50. http://dx.doi.org/10.1007/bf02577147.

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Aramova, Annetta G. "Symmetric products of Gorenstein varieties." Journal of Algebra 146, no. 2 (March 1992): 482–96. http://dx.doi.org/10.1016/0021-8693(92)90079-2.

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Dissertations / Theses on the topic "Symmetric varieties"

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Esposito, Francesco. "Orbits in symmetric varieties." Doctoral thesis, La Sapienza, 2005. http://hdl.handle.net/11573/917110.

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Young, Ian David. "Symmetric squares of modular Abelian varieties." Thesis, University of Sheffield, 2008. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.500087.

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mazzon, andrea. "Hilbert functions and symmetric tensors identifiability." Doctoral thesis, Università di Siena, 2021. http://hdl.handle.net/11365/1133145.

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We study the Waring decompositions of a given symmetric tensor using tools of algebraic geometry for the study of finite sets of points. In particular we use the properties of the Hilbert functions and the Cayley-Bacharach property to study the uniqueness of a given decomposition (the identifiability problem), and its minimality, and show how, in some cases, one can effectively determine the uniqueness even in some range in which the Kruskal's criterion does not apply. We give also a more efficient algorithm that, under some hypothesis, certify the identifiability of a given symmetric tensor.
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Mbirika, Abukuse III. "Analysis of symmetric function ideals: towards a combinatorial description of the cohomology ring of Hessenberg varieties." Diss., University of Iowa, 2010. https://ir.uiowa.edu/etd/708.

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Symmetric functions arise in many areas of mathematics including combinatorics, topology and algebraic geometry. Using ideals of symmetric functions, we tie these three branches together. This thesis generalizes work of Garsia and Procesi in 1992 that gave a quotient ring presentation for the cohomology ring of Springer varieties. Let R be the polynomial ring Ζ[x1,…,xn]. We present two different ideals in R. Both are parametrized by a Hessenberg function h, namely a nondecreasing function that satisfies h(i) ≥ i for all i. The first ideal, which we call Ih, is generated by modified elementary symmetric functions. The ideal I_h generalizes the work of Tanisaki who gave a combinatorial description of the ideal used in Garsia and Procesi's quotient ring. Like the Tanisaki ideal, the generating set for Ih is redundant. We give a minimal generating set for this ideal. The second ideal, which we call Jh, is generated by modified complete symmetric functions. The generators of this ideal form a Gröbner basis, which is a useful property. Using the Gröbner basis for Jh, we identify a basis for the quotient R/Jh. We introduce a partial ordering on the Hessenberg functions, and in turn we discover nice nesting properties in both families of ideals. When h>h', we have Ih ⊂ Ih' and Jh ⊂ Jh'. We prove that Ih equals Jh when h is maximal. Since Ih is the ideal generated by the elementary symmetric functions when h is maximal, the generating set for Jh forms a Gröbner basis for the elementary symmetric functions. Moreover, the quotient R/Jh gives another description of the cohomology ring of the full flag variety. The generators of the ring R/Jh are in bijective correspondence with the Betti numbers of certain Hessenberg varieties. These varieties are a two-parameter generalization of Springer varieties, parametrized by a nilpotent operator X and a Hessenberg function h. These varieties were introduced in 1992 by De Mari, Procesi and Shayman. We provide evidence that as h varies, the quotient R/Jh may be a presentation for the cohomology ring of a subclass of Hessenberg varieties called regular nilpotent varieties.
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Shu, Cheng. "E-Polynomial of GLn⋊<σ>-character varieties." Thesis, Université de Paris (2019-....), 2020. http://www.theses.fr/2020UNIP7038.

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Soit σ l'automorphisme par transpose-inverse de GLn, qui définit un produit semi-direct GLn⋊<σ>. Soit Y→X un revê-tement double de surfaces de Riemann, qui est exactement la partie non ramifiée d'un revêtement ramifié de surfaces de Riemann compactes. L'élément non trivial de Gal(Y/X) sera noté τ. A chaque point ramifié enlevé, on associe une GLn(C)-classe de conjugaison contenue dans la composante connexe GLn(C).σ, et on exige que la famille C des classes de conjugaison soient générique. La variété de GLn(C)⋊<σ>-caractère que l'on a étudié est l'espace de module des pairs (L,Φ) formés d'un système local L sur Y et d'un isomorphisme Φ:L → τ*L*, dont les monodromies autour des points ramifiés sont déterminées par C. On calcule le E-polynôme de cette variété de caractère. A ce fin, on utilise un théorème de Katz, ce qui nous ramème au comptage des points sur corps finis. La formule de comptage fait intervenir les caractères irréductibles de GL_n(q)⋊<σ>, et donc la table des l-adic caractères de ce groupe est déterminée au fur et à mesure. Le polynôme qui en résulte s'exprime comme un produit scalaire de certaines fonctions symétriques associées au produit de couronne (Z/2Z)^N⋊(S_N), avec N=[n/2]
Let σ be the transpose-inverse automorphism of GLn so that we have a semi-direct product GLn⋊<σ>. Let Y→X be a double covering of Riemann surfaces, which is exactly the unramified part of a ramified covering of compact Riemann surfaces. The non trivial covering transformation is denoted by τ. To each puncture (removed ramification point), we prescribe a GLn(C)-conjugacy class contained in the connected component GLn(C).σ . And we require the collection C of these conjugacy classes to be generic. Our GLn(C)⋊<σ>-character variety is the moduli of the pairs (L,Φ), where L is a local system on Y and Φ:L → τ*L* is an isomorphism, whose monodromy at the punctures are determined by C. We compute the E-polynomial of this character variety. To this end, we use a theorem of Katz and translate the problem to point-counting over finite fields. The counting formula involves the irreducible characters of GL_n(q)⋊<σ>, and so the l-adic character table of GL_n(q)⋊<σ> is determined along the way. The resulting polynomial is expressed as the in-ner product of certain symmetric functions associated to the wreath product (Z/2Z)^N⋊(S_N), with N=[n/2]
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Chen, Jiaming. "Topology at infinity and atypical intersections for variations of Hodge structures." Thesis, Université de Paris (2019-....), 2020. http://www.theses.fr/2020UNIP7049.

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Cette thèse étudie les aspects topologiques et géométriques de certains espaces intéressants issus de la théorie de Hodge, tels que les variétés localement symétriques, et leur généralisation, les variétés de Hodge ; ainsi que les applications de périodes qui y prennent valeur.Au chapitre 1 (travail commun avec Looijenga), nous étudions la compactification de Baily-Borel des variétés localement symétriques et ses variantes toroïdales, ainsi que la compactification de Deligne-Mumford de l’espace de module des courbes d’un point de vue topologique. Nous définissons un "type d’homotopie champêtre" pour ces espaces comme le type d’homotopie d’une petite catégorie. Nous généralisons ainsi un ancien résultat de Charney-Lee sur la compactification de Baily-Borel de Ag et récupérons (et reformulons) un résultat plus récent d’Ebert-Giansiracusa sur les compactifications de Deligne-Mumford. Nous décrivons également en ces termes une extension de l’application de périodes pour les surfaces de Riemann. Dans le chapitre 2 (travail commun avec Looijenga), nous donnons une preuve algébro-géométrique relativement simple d’un autre résultat de Charney et Lee sur la cohomologie stable de la compactification de Satake-Baily-Borel de Ag et montrons que cette cohomologie stable est munie d’une structure de Hodge mixte dont nous déterminons les nombres de Hodge.Dans le chapitre 3 (chapitre principal de cette thèse), nous étudions un problème d’intersections atypiques pour une variation de structures de Hodge V sur une variété quasi-projective complexe irréductible lisse S. Nous montrons que l’union des sousvariétés spéciales non-facteur pour (S,V), qui sont de type Shimura avec des applications de périodes dominantes, est une union finie de sous-variétés spéciale des S. Ceci démontre une conjecture de Klingler
This thesis studies topological and geometrical aspects of some interesting spaces springing from Hodge theory, such as locally symmetric varieties, and their generalization, Hodge varieties; and the period maps which take value in them.In Chapter 1 (joint work with Looijenga) we study the Baily-Borel compactifications of locally symmetric varieties and its toroidal variants, as well as the Deligne-Mumford compactification of the moduli of curves from a topological viewpoint. We define a "stacky homotopy type" for these spaces as the homotopy type of a small category and thus generalize an old result of Charney-Lee on the Baily-Borel compactificationof Ag and recover (and rephrase) a more recent one of Ebert-Giansiracusa on the Deligne-Mumford compactification. We also describe an extension of the period map for Riemann surfaces in these terms.In Chapter 2 (joint work with Looijenga) we give a relatively simple algebrogeometric proof of another result of Charney and Lee on the stable cohomology of the Satake-Baily-Borel compactification of Ag and show that this stable cohomology comes with a mixed Hodge structure of which we determine the Hodge numbers.In Chapter 3 (themain chapter of this thesis) we study an atypical intersection problem for an integral polarized variation of Hodge structure V on a smooth irreducible complex quasi-projective variety S. We show that the union of the non-factor special subvarieties for (S,V), which are of Shimura type with dominant period maps, is a finite union of special subvarieties of S. This proves a conjecture of Klingler
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Menes, Thibaut. "Grandes valeurs des formes de Maass sur des quotients compacts de grassmanniennes hyperboliques dans l’aspect volume." Electronic Thesis or Diss., Paris 13, 2024. http://www.theses.fr/2024PA131059.

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Soient n > m = 1 des entiers tels que n + m >= 4 soit pair. On prouve l’existence, dans l’aspect volume, de formes de Maass exceptionnelles sur des quotients compacts de la grassmanienne hyperbolique de signature (n,m). La méthode repose sur le travail de Rudnick et Sarnak, étendu par Donnelly puis généralisé par Brumley et Marshall en rang supérieur. Celle-ci combine un argument de comptage et une relation de périodes permettant de montrer qu’une certaine période distingue les relèvements thêta depuis un groupe auxiliaire. La structure de niveau est définie relativement à cette période et le groupe auxiliaire qui intervient est U(m,m) ou Sp_2m(R), de sorte que (U(n,m),U(m,m)) ou (O(n,m),Sp_2m(R)) soit une paire duale réductive de type 1. La borne inférieure s’exprime naturellement, à un facteur logarithmique près, comme le quotient des volumes avec la structure de congruence principale sur le groupe auxiliaire
Let n > m = 1 be integers such that n + m >= 4 is even. We prove the existence, in the volume aspect, of exceptional Maass forms on compact quotients of the hyperbolic Grassmannian of signature (n,m). The method builds upon the work of Rudnick and Sarnak, extended by Donnelly and then generalized by Brumley and Marshall to higher rank. It combines a counting argument with a period relation, showingthat a certain period distinguishes theta lifts from an auxiliary group. The congruence structure is defined with respect to this period and the auxiliary group is either U(m,m) or Sp_2m(R), making (U(n,m),U(m,m)) or (O(n,m),Sp_2m(R)) a type 1 dual reductive pair. The lower bound is naturally expressed, up to a logarithmic factor, as the ratio of the volumes, with the principal congruence structure on the auxiliary group
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Petracci, Andrea. "On Mirror Symmetry for Fano varieties and for singularities." Thesis, Imperial College London, 2017. http://hdl.handle.net/10044/1/55877.

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In this thesis we discuss some aspects of Mirror Symmetry for Fano varieties and toric singularities. We formulate a conjecture that relates the quantum cohomology of orbifold del Pezzo surfaces to a power series that comes from Fano polygons. We verify this conjecture in some cases, in joint work with A. Oneto. We generalise the Altmann–Mavlyutov construction of deformations of toric singularities: from Minkowski sums of polyhedra we construct deformations of affine toric pairs. Moreover, we propose an approach to the study of deformations of Gorenstein toric singularities of dimension 3 in the context of the Gross–Siebert program. We construct deformations of polarised projective toric varieties by deforming their affine cones. This method is explicit in terms of Cox coordinates and it allows us to give explicit equations for a construction, due to Ilten, which produces a deformation between two toric Fano varieties when their corresponding polytopes are mutation equivalent. We also provide examples of Gorenstein toric Fano 3-folds which are locally smoothable, but not globally smoothable.
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Prince, Thomas. "Applications of mirror symmetry to the classification of Fano varieties." Thesis, Imperial College London, 2016. http://hdl.handle.net/10044/1/43374.

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In this dissertation we discuss two new constructions of Fano varieties, each directly inspired by ideas in Mirror Symmetry. The first recasts the Fanosearch program (Coates--Corti--Kasprzyk et al.) for surfaces in terms of a construction related to the SYZ conjecture. In particular we construct Q-Gorenstein smoothings of toric varieties via an application of the Gross-Siebert algorithm to certain affine manifolds. We recover the theory of combinatorial mutation, which plays a central role in the Fanosearch program, from these affine manifolds. Combining this construction and the work of Gross--Hacking--Keel on log Calabi--Yau surfaces we produce a cluster structure on the mirror to a log del Pezzo surface proposed by Coates--Corti--et al. We exploit the cluster structure, and the connection to toric degenerations, to prove two classification results for Fano polygons. This cluster variety is equipped with a superpotential defined on each chart by a so-called maximally mutable Laurent polynomial. We study an enumerative interpretation of this superpotential in terms of tropical disc counting in the example of the projective plane (with a general choice of boundary divisor). In the second part we develop a new construction of Fano toric complete intersections in higher dimensions. We first consider the problem of finding torus charts on the Hori--Vafa/Givental model, adapting the approach taken by Przyjalkowski. We exploit this to identify 527 new families of four-dimensional Fano manifolds. We then develop an inverse algorithm, Laurent Inversion, which decorates a Fano polytope P with additional information used to construct a candidate ambient space for a complete intersection model of the toric variety defined by P. Moving in the linear system defining this complete intersection allows us to construct new models of known Fano manifolds, and also to construct new examples of Fano manifolds from conjectured mirror Laurent polynomials. We use this algorithm to produce families simultaneously realising certain collections of 'commuting' mutations, extending the connection between polytope mutation and deformations of toric varieties.
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Li, Binru [Verfasser], and Fabrizio [Akademischer Betreuer] Catanese. "Moduli spaces of varieties with symmetries / Binru Li. Betreuer: Fabrizio Catanese." Bayreuth : Universität Bayreuth, 2016. http://d-nb.info/1113107324/34.

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Books on the topic "Symmetric varieties"

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Manivel, Laurent. Symmetric functions, Schubert polynomials, and degeneracy loci. Providence, RI: American Mathematical Society, 2001.

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Fukaya, Kenji. Lagrangian Floer theory and mirror symmetry on compact toric manifolds. Paris: Société Mathématique de France, 2016.

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Noriko, Yui, Yau Shing-Tung 1949-, Lewis James Dominic 1953-, and Banff International Research Station for Mathematics Innovation & Discovery., eds. Mirror symmetry V: Proceedings of the BIRS workshop on Calabi-Yau varieties and mirror symmetry, December 6-11, 2003, Banff International Research Station for Mathematics Innovation & Discovery. Providence, R.I: American Mathematical Society, 2006.

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Rodríguez, Rubí E., 1953- editor of compilation, ed. Riemann and Klein surfaces, automorphisms, symmetries and moduli spaces: Conference in honor of Emilio Bujalance on Riemann and Klein surfaces, symmetries and moduli spaces, June 24-28, 2013, Linköping University, Linköping, Sweden. Providence, Rhode Island: American Mathematical Society, 2014.

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On complete symmetric varieties. 1989.

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Mumford, David, Avner Ash, Michael Rapoport, and Yung-sheng Tai. Smooth Compactifications of Locally Symmetric Varieties. Cambridge University Press, 2010.

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Mumford, David, Avner Ash, Michael Rapoport, and Yung-sheng Tai. Smooth Compactifications of Locally Symmetric Varieties. Cambridge University Press, 2010.

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Mumford, David, Avner Ash, Michael Rapoport, and Yung-sheng Tai. Smooth Compactifications of Locally Symmetric Varieties. Cambridge University Press, 2010.

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Mumford, David, Avner Ash, Michael Rapoport, and Yung-sheng Tai. Smooth Compactifications of Locally Symmetric Varieties. Cambridge University Press, 2010.

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Smooth compactifications of locally symmetric varieties. 2nd ed. Cambridge, UK: Cambridge University Press, 2010.

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Book chapters on the topic "Symmetric varieties"

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Fulton, William, and Piotr Pragacz. "Symmetric polynomials useful in geometry." In Schubert Varieties and Degeneracy Loci, 26–39. Berlin, Heidelberg: Springer Berlin Heidelberg, 1998. http://dx.doi.org/10.1007/bfb0096383.

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Krashen, Daniel, and David J. Saltman. "Severi—Brauer Varieties and Symmetric Powers." In Encyclopaedia of Mathematical Sciences, 59–70. Berlin, Heidelberg: Springer Berlin Heidelberg, 2004. http://dx.doi.org/10.1007/978-3-662-05652-3_5.

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Dijkgraaf, Robbert. "Fields, Strings, Matrices and Symmetric Products." In Moduli of Curves and Abelian Varieties, 151–99. Wiesbaden: Vieweg+Teubner Verlag, 1999. http://dx.doi.org/10.1007/978-3-322-90172-9_8.

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Helminck, A. G. "On Orbit Decompositions for Symmetric k-Varieties." In Symmetry and Spaces, 83–127. Boston: Birkhäuser Boston, 2009. http://dx.doi.org/10.1007/978-0-8176-4875-6_6.

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Hain, Richard. "Locally Symmetric Families of Curves and Jacobians." In Moduli of Curves and Abelian Varieties, 91–108. Wiesbaden: Vieweg+Teubner Verlag, 1999. http://dx.doi.org/10.1007/978-3-322-90172-9_5.

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Mumford, David. "A New Approach to Compactifying Locally Symmetric Varieties." In Selected Papers, 571–84. New York, NY: Springer New York, 2004. http://dx.doi.org/10.1007/978-1-4757-4265-7_19.

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Popov, Vladimir L., and Evgueni A. Tevelev. "Self-dual Projective Algebraic Varieties Associated With Symmetric Spaces." In Encyclopaedia of Mathematical Sciences, 131–67. Berlin, Heidelberg: Springer Berlin Heidelberg, 2004. http://dx.doi.org/10.1007/978-3-662-05652-3_8.

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Ciubotaru, Dan, Kyo Nishiyama, and Peter E. Trapa. "Regular Orbits of Symmetric Subgroups on Partial Flag Varieties." In Representation Theory, Complex Analysis, and Integral Geometry, 61–86. Boston: Birkhäuser Boston, 2011. http://dx.doi.org/10.1007/978-0-8176-4817-6_4.

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Tai, Hsin-sheng. "A class of symmetric functions and Chern classes of projective varieties." In Lecture Notes in Mathematics, 261–74. Berlin, Heidelberg: Springer Berlin Heidelberg, 1989. http://dx.doi.org/10.1007/bfb0087539.

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Helminck, Aloysius. "Combinatorics related to orbit closures of symmetric subgroups in flag varieties." In CRM Proceedings and Lecture Notes, 71–90. Providence, Rhode Island: American Mathematical Society, 2004. http://dx.doi.org/10.1090/crmp/035/05.

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Conference papers on the topic "Symmetric varieties"

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Ghorashi, Ali, Sachin Vaidya, Mikael C. Rechtsman, Wladimir A. Benalcazar, Marin Soljačić, and Thomas Christensen. "Is Photonic Band Topology Common?" In CLEO: Fundamental Science, FW3M.8. Washington, D.C.: Optica Publishing Group, 2024. http://dx.doi.org/10.1364/cleo_fs.2024.fw3m.8.

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Yes. Using high-throughput screening of randomly generated samples, we determine how symmetry, dielectric contrast, and other design parameters influence the prevalence of two-dimensional photonic crystal band topology, across stable, fragile, and higher-order topological varieties.
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Makam, Visu, and Avi Wigderson. "Symbolic determinant identity testing (SDIT) is not a null cone problem; and the symmetries of algebraic varieties." In 2020 IEEE 61st Annual Symposium on Foundations of Computer Science (FOCS). IEEE, 2020. http://dx.doi.org/10.1109/focs46700.2020.00086.

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