A Note on Seshadri constants on general <i>K</i>3 surfaces

Andreas Leopold Knutsen

doi:10.1016/j.crma.2008.09.008

Algebraic Geometry

A Note on Seshadri constants on general K3 surfaces

Presented by: Jean-Pierre Demailly

Andreas Leopold Knutsen ¹

¹ Department of Mathematics, University of Bergen, Johs. Brunsgt. 12, N-5008 Bergen, Norway

Comptes Rendus. Mathématique, Volume 346 (2008) no. 19-20, pp. 1079-1081.

Abstract
Résumé

We prove a lower bound on the Seshadri constant $ε (L)$ on a K3 surface S with $Pic S ≃ Z [L]$ . In particular, we obtain that $ε (L) = α$ if $L^{2} = α^{2}$ for an integer α.

Nous démontrons une borne inférieure sur la constante de Seshadri $ε (L)$ sur un surface K3 telle que $Pic S ≃ Z [L]$ . En particulier, nous obténons que $ε (L) = α$ si $L^{2} = α^{2}$ pour un nombre entier α.

Received: 2007-03-28
Accepted: 2008-09-04
Published online: 2008-09-23

DOI: 10.1016/j.crma.2008.09.008

Author's affiliations:

Andreas Leopold Knutsen ¹

¹ Department of Mathematics, University of Bergen, Johs. Brunsgt. 12, N-5008 Bergen, Norway

@article{CRMATH_2008__346_19-20_1079_0,
     author = {Andreas Leopold Knutsen},
     title = {A {Note} on {Seshadri} constants on general {\protect\emph{K}3} surfaces},
     journal = {Comptes Rendus. Math\'ematique},
     pages = {1079--1081},
     publisher = {Elsevier},
     volume = {346},
     number = {19-20},
     year = {2008},
     doi = {10.1016/j.crma.2008.09.008},
     language = {en},
}

TY  - JOUR
AU  - Andreas Leopold Knutsen
TI  - A Note on Seshadri constants on general K3 surfaces
JO  - Comptes Rendus. Mathématique
PY  - 2008
SP  - 1079
EP  - 1081
VL  - 346
IS  - 19-20
PB  - Elsevier
DO  - 10.1016/j.crma.2008.09.008
LA  - en
ID  - CRMATH_2008__346_19-20_1079_0
ER  -

%0 Journal Article
%A Andreas Leopold Knutsen
%T A Note on Seshadri constants on general K3 surfaces
%J Comptes Rendus. Mathématique
%D 2008
%P 1079-1081
%V 346
%N 19-20
%I Elsevier
%R 10.1016/j.crma.2008.09.008
%G en
%F CRMATH_2008__346_19-20_1079_0

Andreas Leopold Knutsen. A Note on Seshadri constants on general K3 surfaces. Comptes Rendus. Mathématique, Volume 346 (2008) no. 19-20, pp. 1079-1081. doi : 10.1016/j.crma.2008.09.008. https://comptes-rendus.academie-sciences.fr/mathematique/articles/10.1016/j.crma.2008.09.008/

References
Cited by

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

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

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

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

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

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

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

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

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

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

Cited by Sources:

^⁎ 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.

Comments - Politique