Salem Numbers and Enriques Surfaces

References

• [Avritzer and Lange 02] D. Avritzer and H. Lange. “Curves of Genus 2 and Desargues Configurations.” Adv. Geom. 2 (2002), 259–280.
   Web of Science ®Google Scholar
• [Cantat 11] S. Cantat. “Sur les Groupes de Transformations Birationnelles des Surfaces.” Ann. Math. (2) 174 (2011), 299–340.
   Google Scholar
• [Cantat 14] S. Cantat. Dynamics of automorphisms of compact complex surfaces. Frontiers in complex dynamics, 463–514, Princeton Math. Ser., 51, Princeton Univ. Press, Princeton, NJ, 2014.
   Google Scholar
• [Cantat and Dolgachev 12] S. Cantat and I. Dolgachev. “Rational Surfaces with a Large Group of Automorphisms.” J. Amer. Math. Soc. 25 (2012), 863–905.
   Web of Science ®Google Scholar
• [Coble 19] A. Coble. “The Ten Nodes of the Rational Sextic and of the Cayley Symmetroid.” Amer. J. Math. 41 (1919), 243–265.
   Google Scholar
• [Cossec and Dolgachev 89] F. Cossec and I. Dolgachev. Enriques Surfaces. I. Progress in Mathematics, 76. Boston, MA: Birkhäuser Boston, Inc., 1989.
   Google Scholar
• [Dardanelli and van Geemen 07] E. Dardanelli and B. van Geemen. Hessians and the moduli space of cubic surfaces. Algebraic geometry, 17–36, Contemp. Math., 422, Amer. Math. Soc., Providence, RI, 2007.
   Google Scholar
• [Dolgachev and Zhang 01] I. Dolgachev and De-Qi Zhang. “Coble Rational Surfaces.” Amer. J. Math. 123 (2001), 79–114.
   Web of Science ®Google Scholar
• [Dolgachev and Keum 02] I. Dolgachev and J. Keum. “Birational Automorphisms of Quartic Hessian Surfaces.” Trans. Amer. Math. Soc. 354 (2002), 3031–3057.
   Web of Science ®Google Scholar
• [Dolgachev 12] I. Dolgachev. Classical Algebraic Geometry. A Modern View. Cambridge: Cambridge University Press, 2012.
   Google Scholar
• [Dolgachev 16a] I. Dolgachev. A brief introduction to Enriques surfaces, Development of Moduli Theory-Kyoto 2013, Adv. Study in Pure Math. Math. Soc. 69, Math. Soc. Japan, 2016, pp. 1–32.
   Google Scholar
• [Dolgachev 13] I. Dolgachev. “Numerical Automorphisms of Enriques Surfaces in Arbitrary Characteristic, Arithmetic and Geometry of K3 Surfaces and Calabi-Yau Threefold.” In Fields Institute Communications, edited by R. Lazu, M. Schütt, N. Yui, vol. 67, pp. 267–284. New York: Springer, 2013.
   Google Scholar
• [Dolgachev 16b] I. Dolgachev. “Orbital Counting of Curves on Algebraic Surfaces and Sphere Packings, K3 Surfaces and their Modules.” In Progress in Math. 315, edited by C. Faber, G. Farkas, and G. van der Geer, pp. 17–54. Birkhaüser/Springer, 2016.
   Google Scholar
• [Gizatullin 80] M. Gizatullin. “Rational G-surfaces.” Izv. Akad. Nauk SSSR Ser. Mat. 44 (1980), 110–144, 239.
   Google Scholar
• [Hilbert and Cohn-Vossen 32] D. Hilbert and S. Cohn-Vossen. Anschauliche Geometrie. Berlin: Springer, 1932.
   Google Scholar
• [Kondō 86] S. Kondō. “Enriques Surfaces with Finite Automorphism Group.” Japan J. Math. 12 (1986), 192–282.
   Google Scholar
• [McMullen 02] C. McMullen. “Coxeter Groups, Salem Numbers and the Hilbert Metric.” Publ. Math. Inst. Hautes Études Sci. 95 (2002), 151–183.
   Google Scholar
• [McMullen 07] C. McMullen. “Dynamics on Blowups of the Projective Plane.” Publ. Math. Inst. Hautes .tudes Sci. 105 (2007), 49–89.
   Google Scholar
• [McMullen 16] C. McMullen. “Automorphisms of Projective K3 Surfaces with Minimum Entropy.” Invent. Math. 203: 1 (2016), 17–215.
   Web of Science ®Google Scholar
• [Morrison 81] D. Morrison. “Semistable Degenerations of Enriques’ and Hyperelliptic Surfaces.” Duke Math. J. 48 (1981), 197–249.
   Web of Science ®Google Scholar
• [Mukai and Namikawa 84] S. Mukai and Y. Namikawa. “Automorphisms of Enriques Surfaces which Act Trivially on the Cohomology Groups.” Invent. Math. 77 (1984), 383–397.
   Web of Science ®Google Scholar
• [Mukai and Ohashi 15] S. Mukai and H. Ohashi. The Automorphism Groups of Enriques Surfaces Covered by Symmetric Quartic Surfaces. In Recent Advances in Geometry, 307–320. London Math. Soc. Lecture Note Ser., 417. Cambridge: Cambridge University Press, 2015.
   Google Scholar
• [Mukai 10] S. Mukai. “Numerically Trivial Involutions of Kummer Type of an Enriques Surface.” Kyoto J. Math. 50 (2010), 889–902.
   Web of Science ®Google Scholar
• [Oguiso 10] K. Oguiso. The third smallest Salem number in automorphisms of K3 surfaces. Algebraic geometry in East Asia–Seoul 2008, 331–360, Adv. Stud. Pure Math., 60, Math. Soc. Japan, Tokyo, 2010.
   Google Scholar
• [Shimada 16] I. Shimada. “Automorphisms of Supersingular K3 Surfaces and Salem Polynomials.” Exp. Math. 25 (2016), 389–398.
   Web of Science ®Google Scholar
• [Shimada] I. Shimada. “On an Enriques Surface Associated with a Quartic Hessian Surface.” arXiv:1701.00580.
   Google Scholar
• [Sterk 85] H. Sterk. “Finiteness Results for Algebraic K3 Surfaces.” Math. Z. 189 (1985), 507–513.
   Web of Science ®Google Scholar
• [Sullivan 84] D. Sullivan. “Entropy, Hausdorff Measures Old and New, and Limit Sets of Geometrically Finite Kleinian Groups.” Acta Math. 153 (1984), 259–277.
   Web of Science ®Google Scholar
• [Thas 94] J. Thas. “A Rational Sextic Associated with a Desargues Configuration.” Geom. Dedicata 51 (1994), 163–180.
   Web of Science ®Google Scholar
• [Uehara 16] T. Uehara. “Rational Surface Automorphisms with Positive Entropy.” Ann. Inst. Fourier (Grenoble) 66 (2016), 377–432.
   Web of Science ®Google Scholar
• [Veblen 65] O. Veblen and J. W. Young. Projective Geometry. Vol. 1. New York-Toronto-London: Blaisdell Publishing Co. Ginn and Co, 1965.
   Google Scholar
• [Winger 16] R. Winger. “Self-Projective Rational Sextics.” Amer. J. Math. 38: 1 (1916), 45–56.
   Google Scholar
• [Xie 15] J. Xie. “Periodic Points of Birational Transformations on Projective Surfaces.” Duke Math. J. 164 (2015), 903–932.
   Web of Science ®Google Scholar