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Fourier–Mukai Partners and Polarised \(\mathop{\mathrm{K3}}\nolimits\) Surfaces

  • K. Hulek
  • D. Ploog
Chapter
Part of the Fields Institute Communications book series (FIC, volume 67)

Abstract

The purpose of this note is twofold. We first review the theory of Fourier–Mukai partners together with the relevant part of Nikulin’s theory of lattice embeddings via discriminants. Then we consider Fourier–Mukai partners of \(\mathop{\mathrm{K3}}\nolimits\) surfaces in the presence of polarisations, in which case we prove a counting formula for the number of partners.

Key words

K3 surfaces Fourier–Mukai partners Torelli theorem Lattice embeddings 

Mathematics Subject Classifications

Primary 14J28 Secondary 11E12 18E30 

Notes

Acknowledgements

 We thank F. Schulze for discussions concerning lattice theory. We are grateful to M. Schütt and to the referee who improved the article considerably. The first author would like to thank the organisers of the Fields Institute Workshop on Arithmetic and Geometry of \(\mathop{\mathrm{K3}}\nolimits\) surfaces and Calabi–Yau threefolds held in August 2011 for a very interesting and stimulating meeting. The second author has been supported by DFG grant Hu 337/6-1 and by the DFG priority programme 1388 “representation theory”.

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Copyright information

© Springer Science+Business Media New York 2013

Authors and Affiliations

  1. 1.Institut für Algebraische GeometrieLeibniz Universität HannoverHannoverGermany

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