Cylinders in rational surfaces

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Abstract

We answer a question of Ciliberto's about cylinders in rational surfaces obtained by blowing up the plane at points in general position. Bibliography: 13 titles.

About the authors

Ivan Anatol'evich Cheltsov

University of Edinburgh; HSE University

Email: cheltsov@yahoo.com
Doctor of physico-mathematical sciences, Professor

References

  1. I. Cheltsov, “Del Pezzo surfaces and local inequalities”, Automorphisms in birational and affine geometry, Springer Proc. Math. Stat., 79, Springer, Cham, 2014, 83–101
  2. I. Cheltsov, Jihun Park, Joonyeong Won, “Affine cones over smooth cubic surfaces”, J. Eur. Math. Soc. (JEMS), 18:7 (2016), 1537–1564
  3. I. Cheltsov, Jihun Park, Joonyeong Won, “Cylinders in del Pezzo surfaces”, Int. Math. Res. Not. IMRN, 2017:4 (2017), 1179–1230
  4. C. Ciliberto, B. Harbourne, R. Miranda, J. Roe, “Variations on Nagata's conjecture”, A celebration of algebraic geometry, Clay Math. Proc., 18, Amer. Math. Soc., Providence, RI, 2013, 185–203
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  8. T. Kishimoto, Yu. Prokhorov, M. Zaidenberg, “$mathbb{G}_a$-actions on affine cones”, Transform. Groups, 18:4 (2013), 1137–1153
  9. T. Kishimoto, Yu. Prokhorov, M. Zaidenberg, “Unipotent group actions on del Pezzo cones”, Algebraic Geometry, 1:1 (2014), 46–56
  10. J. Kollar, S. Mori, Birational geometry of algebraic varieties, With the collaboration of C. H. Clemens and A. Corti, transl. from the 1998 Japan. original, Cambridge Tracts in Math., 134, Cambridge Univ. Press, Cambridge, 1998, viii+254 pp.
  11. L. Marquand, Joonyeong Won, “Cylinders in rational surfaces”, Eur. J. Math., 4:3 (2018), 1161–1196
  12. Ю. Г. Прохоров, “К проблеме разложения Зариского”, Бирациональная геометрия: линейные системы и конечно порожденные алгебры, Сборник статей, Тр. МИАН, 240, Наука, МАИК «Наука/Интерпериодика», М., 2003, 43–72
  13. F. Sakai, “On polarized normal surfaces”, Manuscripta Math., 59:1 (1987), 109–127

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