Geodesic
Varieties with a~torus action of complexity one having a~finite number of automorphism group orbits
Fundamentalʹnaâ i prikladnaâ matematika, Tome 24 (2023) no. 4, pp. 47-59.

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In this paper, we obtain sufficient conditions for a variety with a torus action of complexity one to have a finite number of automorphism group orbits. 
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S. A. Gaifullin; D. A. Chunaev. Varieties with a~torus action of complexity one having a~finite number of automorphism group orbits. Fundamentalʹnaâ i prikladnaâ matematika, Tome 24 (2023) no. 4, pp. 47-59. https://geodesic-test.mathdoc.fr/item/FPM_2023_24_4_a3/

[1] Arzhantsev I. V., Gaifullin S. A., “Koltsa Koksa, polugruppy i avtomorfizmy affinnykh mnogoobrazii”, Matem. sb., 201:1 (2010), 3–24 | DOI | MR | Zbl

[2] Arzhantsev I. V., Zaidenberg M. G., Kuyumzhiyan K. G., “Mnogoobraziya flagov, toricheskie mnogoobraziya i nadstroiki: tri primera beskonechnoi tranzitivnosti”, Matem. sb., 203:7 (2012), 3–30 | DOI | MR | Zbl

[3] Boldyrev I. A., Gaifullin S. A., “Avtomorfizmy nenormalnykh toricheskikh mnogoobrazii”, Matem. zametki, 110:6 (2021), 837–855 | DOI | Zbl

[4] Arzhantsev I., “On rigidity of factorial trinomial hypersurfaces”, Int. J. Algebra Comput., 26:5 (2016), 1061–1070 | DOI | MR | Zbl

[5] Arzhantsev I., Braun L., Hausen J., Wrobel M., “Log terminal singularities, platonic tuples and iteration of Cox rings”, Eur. J. Math., 4:1 (2018), 242–312 | DOI | MR | Zbl

[6] Arzhantsev I., Derenthal U., Hausen J., Laface A., Cox Rings, Cambridge Stud. Adv. Math., 144, Cambridge Univ. Press, Cambridge, 2015 | MR | Zbl

[7] Arzhantsev I., Flenner H., Kaliman S., Kutzschebauch F., Zaidenberg M., “Flexible varieties and automorphism groups”, Duke Math. J., 162:4 (2013), 767–823 | DOI | MR | Zbl

[8] Arzhantsev I., Gaifullin S., “The automorphism group of a rigid affine variety”, Math. Nachr., 290:5 (2017), 662–671 | DOI | MR | Zbl

[9] Arzhantsev I., Hausen J., Herppich E., Liendo A., “The automorphism group of a variety with torus action of complexity one”, Moscow Math. J., 14:3 (2014), 429–471 | DOI | MR | Zbl

[10] Arzhantsev I., Zaitseva Y., Affine homogeneous varieties and suspensions, 2023, arXiv: 2309.06170 | MR

[11] Evdokimova P., Gaifullin S., Shafarevich A., Rigid trinomial varieties, 2023, arXiv: 2307.06672 | Zbl

[12] Freudenburg G., Algebraic Theory of Locally Nilpotent Derivations, Springer, Berlin, 2017 | MR | Zbl

[13] Gaifullin S., On rigidity of trinomial hypersurfaces and factorial trinomial varieties, 2019, arXiv: 1902.06136

[14] Gayfullin S., Shafarevich A., “Flexibility of normal affine horospherical varieties”, Proc. Amer. Math. Soc., 147 (2019), 3317–3330 | DOI | MR

[15] Gaifullin S., Shirinkin G., Orbits of automorphism group of trinomial hypersurfaces, 2022, arXiv: 2205.02513

[16] Hausen J., Herppich E., “Factorially graded rings of complexity one”, Torsors, “Étale Homotopy and Applications to Rational Points”, London Math. Soc. Lect. Note Ser., 405, Cambridge Univ. Press, Cambridge, 2013, 414–428 | MR | Zbl

[17] Hausen J., Suess H., “The Cox ring of an algebraic variety with torus action”, Adv. Math., 225 (2010), 977–1012 | DOI | MR | Zbl

[18] Hausen J., Wrobel M., “Non-complete rational T-varieties of complexity one”, Math. Nachr., 290:5–6 (2017), 815–826 | DOI | MR | Zbl

[19] Hausen J., Wrobel M., “On iteration of Cox rings”, J. Pure Appl. Algebra, 222:9 (2018), 2737–2745 | DOI | MR | Zbl

[20] Knop F., “The Luna–Vust theory of spherical embeddings”, Proc. of the Hyderabad Conf. on Algebraic Groups (Hyderabad, India, 1989), Manoj Prakashan, Madras, 1991, 225–249 | MR | Zbl

[21] Rentschler R., “Opérations du groupe additif sur le plane affine”, C. R. Acad. Sci., 267 (1968), 384–387 | MR | Zbl

[22] Timashev D. A., Homogeneous Spaces and Equivariant Embeddings, Encycl. Math. Sci., 138, Springer, Berlin, 2011 | MR | Zbl