Article

Manuscripta Mathematica

, Volume 135, Issue 1, pp 215-228

First online:

Open Access This content is freely available online to anyone, anywhere at any time.

On the Seshadri constants of adjoint line bundles

  • Thomas BauerAffiliated withFachbereich Mathematik und Informatik, Philipps-Universität Marburg Email author 
  • , Tomasz SzembergAffiliated withInstytut Matematyki UPAlbert-Ludwigs-Universität Freiburg, Mathematisches Institut

Abstract

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)

14C20