Algebraic Geometry
A Note on Seshadri constants on general K3 surfaces
[Une Note sur les constantes de Seshadri sur surfaces K3 générales]
Comptes Rendus. Mathématique, Tome 346 (2008) no. 19-20, pp. 1079-1081.

Nous démontrons une borne inférieure sur la constante de Seshadri ε(L) sur un surface K3 telle que PicSZ[L]. En particulier, nous obténons que ε(L)=α si L2=α2 pour un nombre entier α.

We prove a lower bound on the Seshadri constant ε(L) on a K3 surface S with PicSZ[L]. In particular, we obtain that ε(L)=α if L2=α2 for an integer α.

Reçu le :
Accepté le :
Publié le :
DOI : 10.1016/j.crma.2008.09.008
Knutsen, Andreas Leopold 1

1 Department of Mathematics, University of Bergen, Johs. Brunsgt. 12, N-5008 Bergen, Norway
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Knutsen, Andreas Leopold. A Note on Seshadri constants on general K3 surfaces. Comptes Rendus. Mathématique, Tome 346 (2008) no. 19-20, pp. 1079-1081. doi : 10.1016/j.crma.2008.09.008. http://www.numdam.org/articles/10.1016/j.crma.2008.09.008/

[1] Bauer, Th. Seshadri constants on algebraic surfaces, Math. Ann., Volume 313 (1999), pp. 547-583

[2] Bauer, Th. Seshadri constants of quartic surfaces, Math. Ann., Volume 309 (1999), pp. 475-481

[3] Bauer, Th.; Di Rocco, S.; Szemberg, T. Generation of jets on K3 surfaces, J. Pure Appl. Algebra, Volume 146 (2000), pp. 17-27

[4] Chen, X. A simple proof that rational curves on K3 are nodal, Math. Ann., Volume 324 (2002), pp. 71-104

[5] Chen, X. Rational curves on K3 surfaces, J. Algebraic Geom., Volume 8 (1999), pp. 245-278

[6] Demailly, J.P. Singular Hermitian metrics on positive line bundles, Bayreuth, 1990 (Lecture Notes in Math.), Volume vol. 1507, Springer, Berlin (1992), pp. 87-104

[7] Kodaira, K. On the structure of compact complex analytic surfaces. I, Amer. J. Math., Volume 86 (1964), pp. 751-798

[8] Lazarsfeld, R. Positivity in algebraic geometry. I. Classical setting: line bundles and linear series, Ergebnisse der Mathematik und ihrer Grenzgebiete. 3. Folge. A Series of Modern Surveys in Mathematics, vol. 48, Springer-Verlag, Berlin, 2004

[9] Oguiso, K. Seshadri constants in a family of surfaces, Math. Ann., Volume 323 (2002), pp. 625-631

[10] Steffens, A. Remarks on Seshadri constants, Math. Z., Volume 227 (1998), pp. 505-510

[11] Szemberg, T. On positivity of line bundles on Enriques surfaces, Trans. Amer. Math. Soc., Volume 353 (2001), pp. 4963-4972

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Research supported by a Marie Curie Intra-European Fellowship within the 6th European Community Framework Programme and carried out at Università di Roma Tre, Rome, Italy.