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Journal articles on the topic 'Symmetric varieties'

Author: Grafiati

Published: 5 April 2025

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1

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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2

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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3

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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4

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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5

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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6

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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7

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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8

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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9

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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10

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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11

Springer, T. A. "Decompositions related to symmetric varieties." Journal of Algebra 329, no. 1 (March 2011): 260–73. http://dx.doi.org/10.1016/j.jalgebra.2010.03.014.

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12

Kiritchenko, Valentina, and Amalendu Krishna. "Equivariant cobordism of flag varieties and of symmetric varieties." Transformation Groups 18, no. 2 (May 5, 2013): 391–413. http://dx.doi.org/10.1007/s00031-013-9223-z.

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13

Lee, Jae-Hyouk, Kyeong-Dong Park, and Sungmin Yoo. "Kähler–Einstein Metrics on Smooth Fano Symmetric Varieties with Picard Number One." Mathematics 9, no. 1 (January 5, 2021): 102. http://dx.doi.org/10.3390/math9010102.

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Symmetric varieties are normal equivarient open embeddings of symmetric homogeneous spaces, and they are interesting examples of spherical varieties. We prove that all smooth Fano symmetric varieties with Picard number one admit Kähler–Einstein metrics by using a combinatorial criterion for K-stability of Fano spherical varieties obtained by Delcroix. For this purpose, we present their algebraic moment polytopes and compute the barycenter of each moment polytope with respect to the Duistermaat–Heckman measure.

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14

Yu, Chenglong, and Zhiwei Zheng. "Moduli spaces of symmetric cubic fourfolds and locally symmetric varieties." Algebra & Number Theory 14, no. 10 (November 19, 2020): 2647–83. http://dx.doi.org/10.2140/ant.2020.14.2647.

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15

Can, Mahir Bilen, Michael Joyce, and Benjamin Wyser. "Wonderful symmetric varieties and Schubert polynomials." Ars Mathematica Contemporanea 15, no. 2 (September 11, 2018): 523–42. http://dx.doi.org/10.26493/1855-3974.1062.ba8.

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16

Pate, Thomas H. "Algebraic varieties in the symmetric algebra." Linear and Multilinear Algebra 20, no. 1 (November 1986): 63–74. http://dx.doi.org/10.1080/03081088608817742.

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17

PANYUSHEV, DMITRI, and OKSANA YAKIMOVA. "Symmetric pairs and associated commuting varieties." Mathematical Proceedings of the Cambridge Philosophical Society 143, no. 2 (September 2007): 307–21. http://dx.doi.org/10.1017/s0305004107000473.

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AbstractLet $\g=\g_0\oplus\g_1$ be a $\mathbb Z_2$-grading of a simple Lie algebra $\g$. The commuting variety associated with such a grading is the variety of pairs of commuting elements from $\g_1$. We study the problem of irreducibility of these varieties. Using invariant-theoretic technique, we present new instances of reducible and irreducible commuting varieties.

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18

Sankaran, G. K. "Fundamental group of locally symmetric varieties." Manuscripta Mathematica 90, no. 1 (December 1996): 39–48. http://dx.doi.org/10.1007/bf02568292.

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19

Strickland, Elisabetta. "Equivariant betti numbers for symmetric varieties." Journal of Algebra 145, no. 1 (January 1992): 120–27. http://dx.doi.org/10.1016/0021-8693(92)90180-t.

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20

Kollár, János. "Symmetric powers of Severi–Brauer varieties." Annales de la faculté des sciences de Toulouse Mathématiques 27, no. 4 (2018): 849–62. http://dx.doi.org/10.5802/afst.1584.

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21

Maffei, Andrea, and Rocco Chiriv�. "Projective normality of complete symmetric varieties." Duke Mathematical Journal 122, no. 1 (March 2004): 93–123. http://dx.doi.org/10.1215/s0012-7094-04-12213-4.

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22

Pumplün, Susanne. "Symmetric composition algebras over algebraic varieties." manuscripta mathematica 132, no. 3-4 (February 22, 2010): 307–33. http://dx.doi.org/10.1007/s00229-010-0348-2.

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23

Buch, Anders Skovsted. "Stanley Symmetric Functions and Quiver Varieties." Journal of Algebra 235, no. 1 (January 2001): 243–60. http://dx.doi.org/10.1006/jabr.2000.8478.

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24

Akhiezer, D. N., and E. B. Vinberg. "Weakly symmetric spaces and spherical varieties." Transformation Groups 4, no. 1 (March 1999): 3–24. http://dx.doi.org/10.1007/bf01236659.

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25

Kinser, Ryan, and Jenna Rajchgot. "Type D quiver representation varieties, double Grassmannians, and symmetric varieties." Advances in Mathematics 376 (January 2021): 107454. http://dx.doi.org/10.1016/j.aim.2020.107454.

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26

AVAN, J., J.-M. MAILLARD, M. TALON, and C. VIALLET. "ALGEBRAIC VARIETIES FOR THE CHIRAL POTTS MODEL." International Journal of Modern Physics B 04, no. 10 (August 1990): 1743–62. http://dx.doi.org/10.1142/s0217979290000875.

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We describe the symmetries of the chiral checkerboard Potts model (duality, inversion relation, …) and write down the algebraic variety corresponding to the integrable case advocated by Baxter, Perk, Au-Yang. We examine some of its subvarieties, in different limits and for various lattices, with a special emphasis on q=3. This yields for q=3, a new algebraic variety where the standard scalar checkerboard Potts model is solvable. By a comparative analysis of the parametrization of the integrable four-state chiral Potts model and the one of the symmetric Ashkin-Teller model, we bring to light algebraic subvarieties for the q-state chiral Potts model which are invariant under the symmetries of the model. We recover in this manner the Fateev-Zamolodchikov points.

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27

Chajda, Ivan. "Varieties with modular and distributive lattices of symmetric or reflexive relations." Czechoslovak Mathematical Journal 42, no. 4 (1992): 623–30. http://dx.doi.org/10.21136/cmj.1992.128357.

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28

Chirivì, Rocco, Corrado De Concini, and Andrea Maffei. "On normality of cones over symmetric varieties." Tohoku Mathematical Journal 58, no. 4 (December 2006): 599–616. http://dx.doi.org/10.2748/tmj/1170347692.

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29

Hemmer, David J., and Daniel K. Nakano. "Support varieties for modules over symmetric groups." Journal of Algebra 254, no. 2 (August 2002): 422–40. http://dx.doi.org/10.1016/s0021-8693(02)00104-7.

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30

Casagrande, Cinzia. "Centrally symmetric generators in toric Fano varieties." manuscripta mathematica 111, no. 4 (August 1, 2003): 471–85. http://dx.doi.org/10.1007/s00229-003-0374-4.

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31

Maffei, Andrea. "Orbits in Degenerate Compactifications of Symmetric Varieties." Transformation Groups 14, no. 1 (November 20, 2008): 183–94. http://dx.doi.org/10.1007/s00031-008-9040-y.

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32

Süß, Hendrik. "Kähler–Einstein metrics on symmetric FanoT-varieties." Advances in Mathematics 246 (October 2013): 100–113. http://dx.doi.org/10.1016/j.aim.2013.06.023.

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33

Gagliardi, Giuliano, and Johannes Hofscheier. "The generalized Mukai conjecture for symmetric varieties." Transactions of the American Mathematical Society 369, no. 4 (May 2, 2016): 2615–49. http://dx.doi.org/10.1090/tran/6738.

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34

Fan, Zhaobing, Chun-Ju Lai, Yiqiang Li, Li Luo, and Weiqiang Wang. "Affine flag varieties and quantum symmetric pairs." Memoirs of the American Mathematical Society 265, no. 1285 (May 2020): 0. http://dx.doi.org/10.1090/memo/1285.

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35

Venkataramana, T. N. "On Cycles on Compact Locally Symmetric Varieties." Monatshefte f?r Mathematik 135, no. 3 (April 1, 2002): 221–44. http://dx.doi.org/10.1007/s006050200018.

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36

Ruzzi, Alessandro. "Projective normality of complete toroidal symmetric varieties." Journal of Algebra 318, no. 1 (December 2007): 302–22. http://dx.doi.org/10.1016/j.jalgebra.2007.07.005.

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37

Franz, Matthias. "Symmetric Products of Equivariantly Formal Spaces." Canadian Mathematical Bulletin 61, no. 2 (June 1, 2018): 272–81. http://dx.doi.org/10.4153/cmb-2017-032-0.

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AbstractLet X be a CW complex with a continuous action of a topological group G. We show that if X is equivariantly formal for singular cohomology with coefficients in some field , then so are all symmetric products of X and in fact all its Γ-products. In particular, symmetric products of quasi-projective M-varieties are again M-varieties. This generalizes a result by Biswas and D’Mello about symmetric products of M-curves. We also discuss several related questions.

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38

Jones, Oliver. "On the geometry of varieties of invertible symmetric and skew-symmetric matrices." Pacific Journal of Mathematics 180, no. 1 (September 1, 1997): 89–100. http://dx.doi.org/10.2140/pjm.1997.180.89.

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39

RUZZI, ALESSANDRO. "SMOOTH PROJECTIVE SYMMETRIC VARIETIES WITH PICARD NUMBER ONE." International Journal of Mathematics 22, no. 02 (February 2011): 145–77. http://dx.doi.org/10.1142/s0129167x11005678.

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We classify the smooth projective symmetric G-varieties with Picard number one (and G semisimple). Moreover, we prove a criterion for the smoothness of the simple (normal) symmetric varieties whose closed orbit is complete. In particular we prove that, given a such variety X which is not exceptional, then X is smooth if and only if an appropriate toric variety contained in X is smooth.

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40

Casarotti, Alex, Alex Massarenti, and Massimiliano Mella. "On Comon’s and Strassen’s Conjectures." Mathematics 6, no. 11 (October 25, 2018): 217. http://dx.doi.org/10.3390/math6110217.

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Comon’s conjecture on the equality of the rank and the symmetric rank of a symmetric tensor, and Strassen’s conjecture on the additivity of the rank of tensors are two of the most challenging and guiding problems in the area of tensor decomposition. We survey the main known results on these conjectures, and, under suitable bounds on the rank, we prove them, building on classical techniques used in the case of symmetric tensors, for mixed tensors. Finally, we improve the bound for Comon’s conjecture given by flattenings by producing new equations for secant varieties of Veronese and Segre varieties.

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41

Boe, Brian D., and Joseph H. G. Fu. "Characteristic Cycles in Hermitian Symmetric Spaces." Canadian Journal of Mathematics 49, no. 3 (June 1, 1997): 417–67. http://dx.doi.org/10.4153/cjm-1997-021-7.

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AbstractWe give explicit combinatorial expresssions for the characteristic cycles associated to certain canonical sheaves on Schubert varieties X in the classical Hermitian symmetric spaces: namely the intersection homology sheaves IHX and the constant sheaves ℂX. The three main cases of interest are the Hermitian symmetric spaces for groups of type An (the standard Grassmannian), Cn (the Lagrangian Grassmannian) and Dn. In particular we find that CC(IHX) is irreducible for all Schubert varieties X if and only if the associated Dynkin diagramis simply laced. The result for Schubert varieties in the standard Grassmannian had been established earlier by Bressler, Finkelberg and Lunts, while the computations in the Cn and Dn cases are new.Our approach is to compute CC(ℂX) by a direct geometric method, then to use the combinatorics of the Kazhdan-Lusztig polynomials (simplified for Hermitian symmetric spaces) to compute CC(IHX). The geometric method is based on the fundamental formula where the Xr ↓ X constitute a family of tubes around the variety X. This formula leads at once to an expression for the coefficients of CC(ℂX) as the degrees of certain singular maps between spheres.

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42

Yohan BRUNEBARBE. "A strong hyperbolicity property of locally symmetric varieties." Annales scientifiques de l'École normale supérieure 53, no. 6 (2020): 1545–60. http://dx.doi.org/10.24033/asens.2453.

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43

Marberg, Eric, and Brendan Pawlowski. "Gröbner geometry for skew-symmetric matrix Schubert varieties." Advances in Mathematics 405 (August 2022): 108488. http://dx.doi.org/10.1016/j.aim.2022.108488.

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44

Browning, T. D., and A. Gorodnik. "Power-free values of polynomials on symmetric varieties." Proceedings of the London Mathematical Society 114, no. 6 (March 10, 2017): 1044–80. http://dx.doi.org/10.1112/plms.12030.

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45

Gorodnik, Alexander, Hee Oh, and Nimish Shah. "Integral points on symmetric varieties and Satake compatifications." American Journal of Mathematics 131, no. 1 (2009): 1–57. http://dx.doi.org/10.1353/ajm.0.0034.

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46

Bigeni, Ange, and Evgeny Feigin. "Symmetric Dellac configurations and symplectic/orthogonal flag varieties." Linear Algebra and its Applications 573 (July 2019): 54–79. http://dx.doi.org/10.1016/j.laa.2019.03.015.

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47

Beelen, Peter, and Prasant Singh. "Linear codes associated to skew-symmetric determinantal varieties." Finite Fields and Their Applications 58 (July 2019): 32–45. http://dx.doi.org/10.1016/j.ffa.2019.03.004.

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48

Robles, C., and D. The. "Rigid Schubert varieties in compact Hermitian symmetric spaces." Selecta Mathematica 18, no. 3 (January 17, 2012): 717–77. http://dx.doi.org/10.1007/s00029-011-0082-y.

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49

TAKAHASHI, NOBUYOSHI. "QUANDLE VARIETIES, GENERALIZED SYMMETRIC SPACES, AND φ-SPACES." Transformation Groups 21, no. 2 (November 25, 2015): 555–76. http://dx.doi.org/10.1007/s00031-015-9351-8.

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50

Richardson, R. W., and T. A. Springer. "Complements to ‘The Bruhat order on symmetric varieties’." Geometriae Dedicata 49, no. 2 (February 1994): 231–38. http://dx.doi.org/10.1007/bf01610623.

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