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http://dx.doi.org/10.7858/eamj.2022.019

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

Won, Joonyeong (Department of Mathematics, Ewha Womans University)
Publication Information
East Asian mathematical journal / v.38, no.3, 2022 , pp. 321-329 More about this Journal
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
del Pezzo surface; alpha invariant; cylinder;
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1 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)
2 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.
3 T. Kishimoto, Yu. Prokhorov, and M. Zaidenberg. Unipotent Group Actions on Del Pezzo Cones, Algebr. Geom. (to appear); arXiv:1212.4479, 11p.
4 Yu. I. Manin, Cubic forms: algebra, geometry, arithmetic, Nauka, Moscow, 1972 (Russian); English transl. North-Holland, Amsterdam, 1974.
5 R. Hartshorne, Algebraic Geometry, Springer-Verlag, New York, 1977.
6 R. Lazarsfeld, Positivity in Algebraic Geometry I. Classical setting: line bundles and linear series, Ergebnisse der Mathematik 48, Springer, 2004.
7 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
8 I.V. Dolgachev, Classical Algebraic Geometry: A Modern View, Cambridge University Press, 2012.
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 I. Arzhantsev, H. Flenner, S. Kaliman, F. Kutzschebauch, M. Zaidenberg, Flexible varieties and automorphism groups, Duke Math. J. 162 (2013), no. 4, 767-823.   DOI
11 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.   DOI
12 I. Cheltsov, J. Park, and J. Won, Affine cones over smooth cubic surfaces, J. Eur. Math. Soc. (JEMS) 18 (2016), no. 7, 15371564.
13 I. Cheltsov, J. Park, and J. Won, : Cylinders in singular del Pezzo surfaces, Compos. Math. 152 (2016), no. 6, 11981224.
14 J. Park, and J. Won, Flexible affine cones over del Pezzo surfaces of degree 4., Eur. J. Math. 2 (2016), no. 1, 304318.