ACM line bundles on polarized K3 surfaces

Abstract

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.

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Acknowledgements

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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Correspondence to Kenta Watanabe.

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Watanabe, K. ACM line bundles on polarized K3 surfaces. Geom Dedicata 203, 321–335 (2019). https://doi.org/10.1007/s10711-019-00436-2

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Keywords

  • ACM line bundle
  • K3 surface
  • Curve

Mathematics Subject Classification (2010)

  • 14J70
  • 14J28
  • 14J60