Abstract
We study Seshadri constants of the canonical bundle on minimal surfaces of general type. First, we prove that if the Seshadri constant ε(K X , x) is between 0 and 1, then it is of the form (m − 1)/m for some integer m ≥ 2. Secondly, we study values of ε(K X , x) for a very general point x and show that small values of the Seshadri constant are accounted for by the geometry of X.
This is a preview of subscription content, log in via an institution to check access.
Similar content being viewed by others
References
Bauer Th. (1999). Seshadri constants on algebraic surfaces. Math. Ann. 313: 547–583
Catanese F. and Pignatelli R. (2006). Fibrations of low genus. I. Ann. Scient. c. Norm. Sup. 39: 1011–1049
Demailly, J.-P.: Singular Hermitian metrics on positive line bundles. Complex algebraic varieties (Bayreuth, 1990), Lect. Notes Math., vol. 1507, pp. 87–104. Springer, Heidelberg (1992)
Ein, L., Lazarsfeld, R.: Seshadri constants on smooth surfaces. In: Journées de Géométrie Algébrique d’Orsay (Orsay, 1992). Astérisque No. 218, pp. 177–186 (1993)
Lazarsfeld R. (2004). Positivity in Algebraic Geometry I. Springer, Heidelberg
Mendes Lopes M. (2004). A note on a theorem of Xiao Gang. Collect. Math. 55: 33–36
Oguiso K. (2002). Seshadri constants in a family of surfaces. Math. Ann. 323: 625–631
Steenbrink, J.: On the Picard group of certain smooth surfaces in weighted projective spaces. In: Algebraic Geometry, Proceedings La Rábida 1981. Lecture Notes in Mathematics, vol. 961, pp. 302–313. Springer, Berlin (1982)
Syzdek, W., Szemberg, T.: Seshadri fibrations of algebraic surfaces. arXiv:0709.2592v1 [math.AG], to appear in: Math. Nachr.
Author information
Authors and Affiliations
Corresponding author
Rights and permissions
About this article
Cite this article
Bauer, T., Szemberg, T. Seshadri constants on surfaces of general type. manuscripta math. 126, 167–175 (2008). https://doi.org/10.1007/s00229-008-0170-2
Received:
Revised:
Published:
Issue Date:
DOI: https://doi.org/10.1007/s00229-008-0170-2