Birational rigidity of G-del Pezzo threefolds of degree 2

Cover Page

Cite item

Full Text

Open Access Open Access
Restricted Access Access granted
Restricted Access Subscription Access

Abstract

We classify nodal rational non-Q">Q-factorial del Pezzo threefolds of degree 2">2 which can be G">G-birationally rigid for some subgroup GAut(X)">GAut(X)

About the authors

Artem Alexeevich Avilov

HSE University

Author for correspondence.
Email: math-net2025_06@mi-ras.ru

References

  1. D. Abramovich, Jianhua Wang, “Equivariant resolution of singularities in characteristic 0”, Math. Res. Lett., 4:2-3 (1997), 427–433
  2. А. А. Авилов, “Автоморфизмы трехмерных многообразий, представимых в виде пересечения двух квадрик”, Матем. сб., 207:3 (2016), 3–18
  3. A. Avilov, “Automorphisms of singular three-dimensional cubic hypersurfaces”, Eur. J. Math., 4:3 (2018), 761–777
  4. А. А. Авилов, “Бирегулярная и бирациональная геометрия двойных накрытий проективного пространства с ветвлением в квартике с 15 обыкновенными двойными точками”, Изв. РАН. Сер. матем., 83:3 (2019), 5–14
  5. I. Cheltsov, Kummer quartic double solids
  6. I. Cheltsov, A. Dubouloz, T. Kishimoto, Toric $G$-solid Fano threefolds
  7. I. Cheltsov, V. Przyjalkowski, C. Shramov, “Which quartic double solids are rational?”, J. Algebraic Geom., 28:2 (2019), 201–243
  8. I. Cheltsov, V. Przyjalkowski, C. Shramov, “Quartic double solids with icosahedral symmetry”, Eur. J. Math., 2:1 (2016), 96–119
  9. I. Cheltsov, C. Shramov, “Five embeddings of one simple group”, Trans. Amer. Math. Soc., 366:3 (2014), 1289–1331
  10. I. Cheltsov, C. Shramov, Cremona groups and the icosahedron, Monogr. Res. Notes Math., CRC Press, Boca Raton, FL, 2016, xxi+504 pp.
  11. I. Cheltsov, C. Shramov, “Three embeddings of the Klein simple group into the Cremona group of rank three”, Transform. Groups, 17:2 (2012), 303–350
  12. I. Cheltsov, C. Shramov, “Finite collineation groups and birational rigidity”, Selecta Math. (N.S.), 25:5 (2019), 71, 68 pp.
  13. I. V. Dolgachev, V. A. Iskovskikh, “Finite subgroups of the plane Cremona group”, Algebra, arithmetic, and geometry: in honor of Yu. I. Manin, v. I, Progr. Math., 269, Birkhäuser Boston, Boston, MA, 2009, 443–548
  14. I. V. Dolgachev, “Abstract configurations in algebraic geometry”, The Fano conference, Univ. Torino, Turin, 2004, 423–462
  15. T. Fujita, “On singular del Pezzo varieties”, Algebraic geometry (L'Aquila, 1988), Lecture Notes in Math., 1417, Springer, Berlin, 1990, 117–128
  16. T. Fujita, “On the structure of polarized manifolds with total deficiency one. I”, J. Math. Soc. Japan, 32:4 (1980), 709–725
  17. T. Fujita, Classification theories of polarized varieties, London Math. Soc. Lecture Note Ser., 155, Cambridge Univ. Press, Cambridge, 1990, xiv+205 pp.
  18. P. Jahnke, Th. Peternell, “Almost del Pezzo manifolds”, Adv. Geom., 8:3 (2008), 387–411
  19. A. Kuznetsov, Yu. Prokhorov, On higher-dimensional del Pezzo varieties
  20. K. Matsuki, Introduction to the Mori program, Universitext, Springer-Verlag, New York, 2002, xxiv+478 pp.
  21. S. Mori, S. Mukai, “Classification of Fano 3-folds with $B_{2}geq 2$”, Manuscripta Math., 36:2 (1981/82), 147–162
  22. Yu. Prokhorov, “$G$-Fano threefolds. I”, Adv. Geom., 13:3 (2013), 389–418
  23. Yu. Prokhorov, “2-elementary subgroups of the space Cremona group”, Automorphisms in birational and affine geometry, Springer Proc. Math. Stat., 79, Springer, Cham, 2014, 215–229
  24. Ю. Г. Прохоров, “O трехмерных $G$-многообразиях Фано”, Изв. РАН. Сер. матем., 79:4 (2015), 159–174
  25. Yu. Prokhorov, “$p$-elementary subgroups of the Cremona group of rank 3”, Classification of algebraic varieties, EMS Ser. Congr. Rep., Eur. Math. Soc., Zürich, 2011, 327–338
  26. Yu. Prokhorov, “Simple finite subgroups of the Cremona group of rank 3”, J. Algebraic Geom., 21:3 (2012), 563–600
  27. Ю. Г. Прохоров, “Особые многообразия Фано рода 12”, Матем. сб., 207:7 (2016), 101–130
  28. Ю. Г. Прохоров, “Эквивариантная программа минимальных моделей”, УМН, 76:3(459) (2021), 93–182
  29. G. Sanna, Rational curves and instantons on the Fano threefold $Y_{5}$, PhD thesis, SISSA, 2014, 120 pp.

Supplementary files

Supplementary Files
Action
1. JATS XML

Copyright (c) 2023 Avilov A.A.

Согласие на обработку персональных данных

 

Используя сайт https://journals.rcsi.science, я (далее – «Пользователь» или «Субъект персональных данных») даю согласие на обработку персональных данных на этом сайте (текст Согласия) и на обработку персональных данных с помощью сервиса «Яндекс.Метрика» (текст Согласия).