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

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Arithmetic and Geometry of K3 Surfaces and Calabi–Yau Threefolds

Part of the book series: Fields Institute Communications ((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.

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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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  1. Institut für Algebraische Geometrie, Leibniz Universität Hannover, Welfengarten 1, 30167, Hannover, Germany

    K. Hulek & D. Ploog

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  1. K. Hulek
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  2. D. Ploog
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Correspondence to K. Hulek .

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Editors and Affiliations

  1. , Mathematics Department, Stony Brook University, N/A, Stony Brook, 11794-3651, New York, USA

    Radu Laza

  2. , Institut für Algebraische Geometrie, Leibniz Universität Hannover, Welfengarten 1, Hannover, 30167, Germany

    Matthias Schütt

  3. , Department of Math & Stats, Queen's University, University Ave., Kingston, K7L 3N6, Ontario, Canada

    Noriko Yui

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Hulek, K., Ploog, D. (2013). Fourier–Mukai Partners and Polarised \(\mathop{\mathrm{K3}}\nolimits\) Surfaces. In: Laza, R., Schütt, M., Yui, N. (eds) Arithmetic and Geometry of K3 Surfaces and Calabi–Yau Threefolds. Fields Institute Communications, vol 67. Springer, New York, NY. https://doi.org/10.1007/978-1-4614-6403-7_11

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