Abstract
We prove that the action of the special automorphism group on affine cones over del Pezzo surfaces of degree 4 and 5 is infinitely transitive.
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I. Arzhantsev, H. Flenner, S. Kaliman, F. Kutzschebauch, and M. Zaidenberg, “Flexible varieties and automorphism groups,” Duke Math. J., 162:4 (2013), 767–823.
I. V. Arzhantsev, M. Zaidenberg, and K. Kuyumzhiyan, “Flag varieties, toric varieties, and suspensions: Three instances of infinite transitivity,” Mat. Sb., 203:7 (2012), 3–30; English transl.: Sb. Math., 203: 7 (2012), 923–949.
I. Cheltsov, J. Park, and J. Won, Affine Cones over Smooth Cubic Surfaces, http://arxiv.org/abs/1303.2648.
I. V. Dolgachev, Classical Algebraic Geometry: Modern View, Cambridge University Press, Cambridge, 2012.
R. Hartshorne, Algebraic Geometry, Springer-Verlag, New York-Heidelberg, 1977.
T. Kishimoto, Yu. Prokhorov, and M. Zaidenberg, “Group actions on affine cones,” in: Affine Algebraic Geometry, CRM Proc. and Lecture Notes, vol. 54, Amer. Math. Soc., Providence, RI, 2011, 123–163.
T. Kishimoto, Yu. Prokhorov, and M. Zaidenberg, “Unipotent group actions on Del Pezzo cones,” J. Algebraic Geometry, in print; http://arxiv.org/abs/1212.4479.
R. Lazarsfeld, Positivity in Algebraic Geometry I. Classical Setting: Line Bundles and Linear Series, Ergebnisse der Mathematik und ihrer Grenzgebiete, vol. 48, Springer-Verlag, 2004.
Yu. I. Manin, Cubic Forms: Algebra, Geometry, Arithmetic, North-Holland, Amsterdam, 1974.
W. A. Stein et al., Sage Mathematics Software (Version 4.6.1). The Sage Development Team, 2011; http://www.sagemath.org.
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Translated from Funktsional’nyi Analiz i Ego Prilozheniya, Vol. 47, No. 4, pp. 45–52, 2013
Original Russian Text Copyright © by A. Yu. Perepechko
This work was supported by the Ministry of Education and Science of Russian Federation, project no. 8214, and by RFBR grant nos. 12-01-00704 and 12-01-31342mol_a.
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Perepechko, A.Y. Flexibility of affine cones over del Pezzo surfaces of degree 4 and 5. Funct Anal Its Appl 47, 284–289 (2013). https://doi.org/10.1007/s10688-013-0035-7
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DOI: https://doi.org/10.1007/s10688-013-0035-7