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The Cone of Curves of K3 Surfaces Revisited

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Birational Geometry, Rational Curves, and Arithmetic

Abstract

The following theorem was proved in [4] over the complex numbers. It turns out that the proof given there works with very small adjustments in arbitrary characteristic.

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References

  1. K. Ireland and M. Rosen, A classical introduction to modern number theory, second ed., Graduate Texts in Mathematics, vol. 84, Springer-Verlag, New York, 1990.

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  2. J. Kollár, Rational curves on algebraic varieties, Ergebnisse der Mathematik und ihrer Grenzgebiete. 3. Folge. A Series of Modern Surveys in Mathematics, vol. 32, Springer-Verlag, Berlin, 1996.

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  3. J. Kollár and S. Mori, Birational geometry of algebraic varieties, Cambridge Tracts in Mathematics, vol. 134, Cambridge University Press, Cambridge, 1998, With the collaboration of C. H. Clemens and A. Corti, Translated from the 1998 Japanese original.

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  4. S. J. Kovács, The cone of curves of a K3 surface, Math. Ann. 300, no. 4, 681–691, (1994).

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Acknowledgements

This paper owes its existence to Max Lieblich who suggested that perhaps the results of [4] also hold in arbitrary characteristic.

The author was supported in part by NSF Grant DMS-0856185 and the Craig McKibben and Sarah Merner Endowed Professorship in Mathematics at the University of Washington.

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Correspondence to Sándor J. Kovács .

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Kovács, S.J. (2013). The Cone of Curves of K3 Surfaces Revisited. In: Bogomolov, F., Hassett, B., Tschinkel, Y. (eds) Birational Geometry, Rational Curves, and Arithmetic. Springer, New York, NY. https://doi.org/10.1007/978-1-4614-6482-2_8

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