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On an automorphism of Hilb[2] of certain K3 surfaces

Part of: Arithmetic problems. Diophantine geometry Surfaces and higher-dimensional varieties

Published online by Cambridge University Press:  19 January 2011

Ekaterina Amerik
Ekaterina Amerik
Affiliation:
Laboratoire de Mathématiques, Université Paris-Sud, Bâtiment 425, 91405 Orsay, France ([email protected]) and MPIM Bonn, Vivatsgasse 7, 53111 Bonn, Germany
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Abstract

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Following some remarks made by O'Grady and Oguiso, the potential density of rational points on the second punctual Hilbert scheme of certain K3 surfaces is proved.

Keywords

K3 surfacepunctual Hilbert schemeinvolutionrational points

MSC classification

Secondary: 14J28: $K3$ surfaces and Enriques surfaces 14J50: Automorphisms of surfaces and higher-dimensional varieties 14G05: Rational points
Type
Research Article
Information
Proceedings of the Edinburgh Mathematical Society , Volume 54 , Issue 1 , February 2011 , pp. 1 - 7
Copyright
Copyright © Edinburgh Mathematical Society 2011

References

1.Amerik, E. and Campana, F., Fibrations méromorphes sur certaines variétés à fibré canonique trivial, Pure Appl. Math. Q. 4(2) (2008), 509–545.CrossRefGoogle Scholar
2.Beauville, A., Some remarks on Kähler manifolds with c 1 = 0, in Classification of algebraic and analytic manifolds (Katata 1982), Progress in Mathematics, Volume 39 (Birkhäuser, Boston, 1983).Google Scholar
3.Beauville, A., Variétés dont la première classe de Chern est nulle, J. Diff. Geom. 18 (1983), 755–782.Google Scholar
4.Bogomolov, F. A. and Tschinkel, Yu., Density of rational points on elliptic K3 surfaces, Asian J. Math. 4 (2000), 351–368.CrossRefGoogle Scholar
5.Hassett, B. and Tschinkel, Yu., Abelian fibrations and rational points on symmetric products, Int. J. Math. 11(9) (2000), 1163–1176.CrossRefGoogle Scholar
6.Maulik, D., Poonen, B. and Voisin, C., Néron-Severi groups under specialization, preprint (arXiv: 0907.4781; 2009).Google Scholar
7.Morrison, D., On K3 surfaces with large Picard number, Invent. Math. 75 (1984), 105–121.CrossRefGoogle Scholar
8.O'Grady, K., Involutions and linear systems on holomorphic symplectic manifolds, Geom. Funct. Analysis 15 (2005), 1223–1274.CrossRefGoogle Scholar
9.Oguiso, K., A remark on dynamical degrees of automorphisms of hyperkähler manifolds, Manuscr. Math. 130 (1) (2009), 101–111.CrossRefGoogle Scholar
10.Pjateckiĭ-Šapiro, I. I. and Šafarevič, I. R., A Torelli theorem for algebraic surfaces of type K3, Math. USSR Izv. 5(3) (1971), 547–588.CrossRefGoogle Scholar
11.Saint-Donat, B., Projective models of K3 surfaces, Am. J. Math. 96 (1974), 602–639.CrossRefGoogle Scholar
12.Verbitsky, M., Cohomology of compact hyperkähler manifolds and applications, Geom. Funct. Analysis 6 (1996), 601–611.CrossRefGoogle Scholar