Manuscripta Mathematica

, Volume 135, Issue 1, pp 215–228

On the Seshadri constants of adjoint line bundles


    • Fachbereich Mathematik und InformatikPhilipps-Universität Marburg
  • Tomasz Szemberg
    • Instytut Matematyki UP
    • Albert-Ludwigs-Universität FreiburgMathematisches Institut

DOI: 10.1007/s00229-010-0418-5


In the present paper we study the possible values of Seshadri constants. While in general every positive rational number appears as the local Seshadri constant of some ample line bundle, we point out that for adjoint line bundles there are explicit lower bounds depending only on the dimension of the underlying variety. In the surface case, where the optimal lower bound is 1/2, we characterize all possible values in the range between 1/2 and 1—there are surprisingly few. As expected, one obtains even more restrictive results for the Seshadri constants of adjoints of very ample line bundles. Finally, we study Seshadri constants of adjoint line bundles in the multi-point setting.

Mathematics Subject Classification (2000)



We would like to thank C. Ciliberto who sparked our interest in studying Seshadri constants in the adjoint setting. Also, we thank G. Heier for helpful remarks on an earlier version of our paper. The second author was partially supported by a MNiSW Grant N N201 388834.

Open Access

This article is distributed under the terms of the Creative Commons Attribution Noncommercial License which permits any noncommercial use, distribution, and reproduction in any medium, provided the original author(s) and source are credited.

Copyright information

© The Author(s) 2010