ACM line bundles on polarized K3 surfaces

  • Kenta WatanabeEmail author
Original Paper


An ACM bundle on a polarized algebraic variety is defined as a vector bundle whose intermediate cohomology vanishes. We are interested in ACM bundles of rank one with respect to a very ample line bundle on a K3 surface. In this paper, we give a necessary and sufficient condition for a non-trivial line bundle \({\mathcal {O}}_X(D)\) on X with \(|D|\ne \emptyset \) and \(D^2\ge L^2-6\) to be an ACM and initialized line bundle with respect to L, for a given K3 surface X and a very ample line bundle L on X.


ACM line bundle K3 surface Curve 

Mathematics Subject Classification (2010)

14J70 14J28 14J60 



The author would like to thank the referee for the creative suggestions and some helpful comments. The author is partially supported by Grant-in-Aid for Scientific Research (16K05101), Japan Society for the Promotion Science.


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Copyright information

© Springer Nature B.V. 2019

Authors and Affiliations

  1. 1.Nihon University, College of Science and TechnologyFunabashi cityJapan

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