East Asian mathematical journal

The Youngnam Mathematical Society (영남수학회)
권호 표지
DOI QR코드

DOI QR Code

FLEXIBILITY OF AFFINE CONES OVER SINGULAR DEL PEZZO SURFACES WITH DEGREE 4

  • Received : 2022.02.26
  • Accepted : 2022.04.03
  • Published : 2022.05.18
Download PDF
⟨ Previous Next ⟩

Abstract

For an ample divisor A of birational type on a singular del Pezzo surface S of degree 4 with A1-singularity, we show that the affine cone of S defined by A is flexible

Keywords

Acknowledgement

The author was supported by the National Research Foundation of Korea (NRF-2020R1A2C1A01008018).

References

  1. I. Arzhantsev, H. Flenner, S. Kaliman, F. Kutzschebauch, M. Zaidenberg, Flexible varieties and automorphism groups, Duke Math. J. 162 (2013), no. 4, 767-823. https://doi.org/10.1215/00127094-2080132
  2. I.V. Arzhantsev, K. Kuyumzhiyan, M. Zaidenberg, Flag varieties, toric varieties, and suspensions: three instances of infinite transitivity, Sbornik: Math. 203 (2012), no. 7, 923-949. https://doi.org/10.1070/SM2012v203n07ABEH004248
  3. Bogomolov, F., Karzhemanov, I., Kuyumzhiyan, K.Unirationality and existence of infinitely transitive models. In: Bogomolov, F., Hassett, B., Tschinkel, Yu. (eds.) Birational Geometry, Rational Curves, and Arithmetic, pp. 7792. Springer, New York (2013)
  4. I. Cheltsov, J. Park, and J. Won, Affine cones over smooth cubic surfaces, J. Eur. Math. Soc. (JEMS) 18 (2016), no. 7, 15371564.
  5. I. Cheltsov, J. Park, and J. Won, : Cylinders in singular del Pezzo surfaces, Compos. Math. 152 (2016), no. 6, 11981224.
  6. I. Cheltsov, J. Park, J. Won, Cylinders in del Pezzo surfaces,to appear Int. Math. Res. Notices. Int. Math. Res. Not. IMRN 2017, no. 4, 11791230.
  7. I.V. Dolgachev, Classical Algebraic Geometry: A Modern View, Cambridge University Press, 2012.
  8. R. Hartshorne, Algebraic Geometry, Springer-Verlag, New York, 1977.
  9. T. Kishimoto, Yu. Prokhorov, M. Zaidenberg, Group actions on affine cones, arXiv:0905.4647v2, 41p.; in: Affine Algebraic Geometry, CRM Proc. and Lecture Notes, vol. 54, Amer. Math. Soc., Providence, RI, 2011, 123-163.
  10. T. Kishimoto, Yu. Prokhorov, and M. Zaidenberg. Unipotent Group Actions on Del Pezzo Cones, Algebr. Geom. (to appear); arXiv:1212.4479, 11p.
  11. R. Lazarsfeld, Positivity in Algebraic Geometry I. Classical setting: line bundles and linear series, Ergebnisse der Mathematik 48, Springer, 2004.
  12. Yu. I. Manin, Cubic forms: algebra, geometry, arithmetic, Nauka, Moscow, 1972 (Russian); English transl. North-Holland, Amsterdam, 1974.
  13. A. Yu. Perepechko, Flexibility of affine cones over del Pezzo surfaces of degree 4 and 5., Funktsional. Anal. i Prilozhen. 47 (2013), no. 4, 4552; translation in Funct. Anal. Appl. 47 (2013), no. 4, 284289
  14. J. Park, and J. Won, Flexible affine cones over del Pezzo surfaces of degree 4., Eur. J. Math. 2 (2016), no. 1, 304318.