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Equivariant geometry of the Segre cubic and the Burkhardt quartic

  • Ivan Cheltsov [1] ; Yuri Tschinkel [2]
    1. [1] University of Edinburgh

      University of Edinburgh

      Reino Unido

    2. [2] Courant Institute, New York, USA
  • Localización: Selecta Mathematica, New Series, ISSN 1022-1824, Vol. 31, Nº. 1, 2025
  • Idioma: inglés
  • DOI: 10.1007/s00029-024-01001-w
  • Enlaces
  • Resumen
    • We study linearizability and stable linearizability of actions of finite groups on the Segre cubic and Burkhardt quartic, using techniques from group cohomology, birational rigidity, and the Burnside formalism

  • Referencias bibliográficas
    • 1. Arap, M., Cutrone, J., Marshburn, N.: On the existence of certain weak Fano threefolds of Picard number two. Math. Scand. 120(1), 68–86...
    • 2. Avilov, A.: Automorphisms of threefolds that can be represented as an intersection of two quadrics. Sb. Math. 207(3), 315–330 (2016)
    • 3. Avilov, A.: Automorphisms of singular three-dimensional cubic hypersurfaces. Eur. J. Math. 4(3), 761–777 (2018)
    • 4. Avilov, A.: On the forms of the Segre cubic. Mat. Zametki 107(1), 3–10 (2020)
    • 5. Blanc, J., Cheltsov, I., Duncan, A., Prokhorov, Y.: Finite quasisimple groups acting on rationally connected threefolds. Math. Proc. Camb....
    • 6. Blanc, J., Lamy, S.: Weak Fano threefolds obtained by blowing-up a space curve and construction of Sarkisov links. Proceedings of the London...
    • 7. Bogomolov, F., Prokhorov, Y.: On stable conjugacy of finite subgroups of the plane Cremona group. I. Cent. Eur. J. Math. 11(12), 2099–2105...
    • 8. Bruin, N., Filatov, E.: Twists of the Burkhardt quartic threefold. Res. Number Theory 8(4), 73,16 (2022)
    • 9. Bruin, N., Nasserden, B.: Arithmetic aspects of the Burkhardt quartic threefold. J. Lond. Math. Soc. 98(3), 536–556 (2018)
    • 10. Calegari, F., Chidambaram, S.: Rationality of twists of the Siegel modular variety of genus 2 and level 3. Proc. Am. Math. Soc. 150(5),...
    • 11. Cheltsov, I.: Kummer quartic double solids. Rend. Circ. Mat. Palermo 72(3), 1993–2023 (2023)
    • 12. Cheltsov, I., Dubouloz, A., Kishimoto, T.: Toric G-solid Fano threefolds. Selecta Math. (N.S.) 29(2), 22–45 (2023)
    • 13. Cheltsov, I., Kuznetsov, A., Shramov, K.: Coble fourfold, S6-invariant quartic threefolds, and WimanEdge sextics. Algebra Number Theory...
    • 14. Cheltsov, I., Park, J.: Cohomological and Geometric Approaches to Rationality Problems. New Perspectives, pp. 75–132. Boston, MA: Birkhäuser...
    • 15. Cheltsov, I., Przyjalkowski, V., Shramov, C.: Burkhardt quartic, Barth sextic, and the icosahedron. Int. Math. Res. Not. IMRN 12, 3683–3703...
    • 16. Cheltsov, I., Sarikyan, A.: Equivariant pliability of the projective space. Sel. Math. 29(5), 71 (2023)
    • 17. Cheltsov, I., Shramov, C.: Three embeddings of the Klein simple group into the Cremona group of rank three. Transform. Groups 17(2), 303–350...
    • 18. Cheltsov, I., Shramov, C.: Five embeddings of one simple group. Trans. Am. Math. Soc. 366(3), 1289–1331 (2014)
    • 19. Cheltsov, I., Shramov, C.: Cremona Groups and the Icosahedron. Monographs and Research Notes in Mathematics. CRC Press, Boca Raton, FL...
    • 20. Cheltsov, I., Shramov, C.: Finite collineation groups and birational rigidity. Sel. Math. 25(5), 71 (2019)
    • 21. Cheltsov, I., Tschinkel, Y., Zhang, Z.: Supporting tables (2023). Available at: https://zhijiazhangz. github.io/BurkSegre.html
    • 22. Cheltsov, I.A.: Birationally rigid Fano varieties. Russ. Math. Surv. 60(5), 875–965 (2005)
    • 23. Chernousov, V., Gille, P., Reichstein, Z.: Resolving G-torsors by abelian base extensions. J. Algebra 296(2), 561–581 (2006)
    • 24. Corti, A.: Factoring birational maps of threefolds after Sarkisov. J. Algebraic Geom. 4, 223 (1995)
    • 25. Corti, A.: Singularities of linear systems and 3-fold birational geometry. In: Explicit Birational Geometry of 3-Folds, pp. 259–312. Cambridge...
    • 26. Cutrone, J.W., Limarzi, M.A., Marshburn, N.A.: A weak Fano threefold arising as a blowup of a curve of genus 5 and degree 8 on P3. Eur....
    • 27. Cutrone, J.W., Marshburn, N.A.: Towards the classification of weak Fano threefolds with ρ = 2. Cent. Eur. J. Math. 11(9), 1552–1576...
    • 28. de Jong, A.J., Shepherd-Barron, N.I., Van de Ven, A.: On the Burkhardt quartic. Math. Ann. 286(1–3), 309–328 (1990)
    • 29. Dolgachev, I.V., Iskovskikh, V.A.: Finite subgroups of the plane Cremona group. In Algebra, arithmetic, and geometry: in honor of Y.I....
    • 30. Finkelnberg, H.: On the geometry of the Burkhardt quartic (1989). Leiden, (Ph.D. thesis)
    • 31. Florence, M., Reichstein, Z.: The rationality problem for forms of M0,n. Bull. Lond. Math. Soc. 50(1), 148–158 (2018)
    • 32. Hacon, C.D., McKernan, J.: The Sarkisov program. J. Algebr. Geom., 22(2), 389–405 (2013)
    • 33. Hassett, B., Kresch, A., Tschinkel, Y.: Symbols and equivariant birational geometry in small dimensions. In: Rationality of Varieties,...
    • 34. Hassett, B., Tschinkel, Y.: On the effective cone of the moduli space of pointed rational curves. In: Topology and Geometry: Commemorating...
    • 35. Hassett, B., Tschinkel, Y.: Rationality of complete intersections of two quadrics over nonclosed fields. Enseign. Math. 67(1–2), 1–44...
    • 36. Hassett, B., Tschinkel, Y.: Equivariant geometry of odd-dimensional complete intersections of two quadrics. Pure Appl. Math. Q. 18(4),...
    • 37. Hassett, B., Tschinkel, Y.: Torsors and stable equivariant birational geometry. Nagoya Math. J. 250, 275–297 (2023)
    • 38. Hoshi, A., Yamasaki, A.: Rationality problem for algebraic tori. Mem. Am. Math. Soc. 248(1176), 215 (2017)
    • 39. Hunt, B.: The Geometry of Some Special Arithmetic Quotients. Lecture Notes in Mathematics, vol. 1637. Springer-Verlag, Berlin (1996)
    • 40. Jahnke, P., Peternell, T., Radloff, I.: Threefolds with big and nef anticanonical bundles. I. Math. Ann. 333(3), 569–631 (2005)
    • 41. Jahnke, P., Peternell, T., Radloff, I.: Threefolds with big and nef anticanonical bundles. II. Cent. Eur. J. Math. 9(3), 449–488 (2011)
    • 42. Kollár, J.: Automorphisms and twisted forms of rings of invariants (2022). arXiv:2212.03772
    • 43. Kresch, A., Tschinkel, Y.: Cohomology of finite subgroups of the plane Cremona group (2022). arXiv:2203.01876
    • 44. Kresch, A., Tschinkel, Y.: Equivariant birational types and Burnside volume. Ann. Sc. Norm. Super. Pisa Cl. Sci. 23(2), 1013–1052 (2022)
    • 45. Kresch, A., Tschinkel, Y.: Equivariant Burnside groups and representation theory. Sel. Math. 28(4), 81 (2022)
    • 46. Kunyavski˘ı, B. È.: Three-dimensional algebraic tori. In: Investigations in number theory (Russian) pp. 90–111. Saratov. Gos. Univ., Saratov...
    • 47. Mella, M.: Birational geometry of quartic 3-folds. II: The importance of being Q-factorial. Math. Ann. 330(1), 107–126 (2004)
    • 48. Mori, S., Mukai, S.: Classification of Fano 3-folds with B 2 ≥ 2. Manuscr. Math. 36(2), 147–162 (1981)
    • 49. Pettersen, K.: On nodal determinental hypersurfaces in P4 (1998). Ph.D. thesis
    • 50. Pinardin, A.: G-solid rational rurfaces (2023). arXiv:2309.13757
    • 51. Prokhorov, Y.: Simple finite subgroups of the Cremona group of rank 3. J. Algebraic Geom. 21(3), 563–600 (2012)
    • 52. Prokhorov, Y.: G-Fano threefolds. II. Adv. Geom. 13(3), 419–434 (2013)
    • 53. Prokhorov, Y.: On birational involutions of P3. Izv. Ross. Akad. Nauk Ser. Mat. 77(3), 199–222 (2013)
    • 54. Prokhorov, Y.: On stable conjugacy of finite subgroups of the plane Cremona group. II. Michigan Math. J. 64(2), 293–318 (2015)
    • 55. Prokhorov, Y.: Finite groups of birational transformations (2021). arXiv:2108.13325
    • 56. Pukhlikov, A.V.: Birational automorphisms of Fano hypersurfaces. Invent. Math. 134(2), 401–426 (1998)
    • 57. Sakovics, D.: G-birational rigidity of the projective plane. Eur. J. Math. 5(3), 1090–1105 (2019)
    • 58. Sarikyan, A.: On linearization problems in the plane Cremona group (2020). arXiv:2009.05761
    • 59. Takeuchi, K.: Some birational maps of Fano 3-folds. Compos. Math. 71(3), 265–283 (1989)
    • 60. Takeuchi, K.: Weak Fano threefolds with del Pezzo fibration. Eur. J. Math. 8(3), 1225–1290 (2022)
    • 61. Todd, J.A.: On a quartic primal with forty-five nodes, in space of four dimensions. Q. J. Math. 7, 168–174 (1936)
    • 62. Tschinkel, Y., Yang, K.: Potentially stably rational del Pezzo surfaces over nonclosed fields. In: Combinatorial and additive number theory....
    • 63. Tschinkel, Y., Yang, K., Zhang, Z.: Combinatorial Burnside groups. Res. Number Theory 8(2), 33 (2022)
    • 64. Tschinkel, Y., Yang, K., Zhang, Z.: Equivariant birational geometry of linear actions (2023). arXiv:2302.02296

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