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The Universal Kummer Threefold

Author: Ardila [Ardila et al. 07] F.
Beauville [Beauville 06] A.
Bourbaki [Bourbaki 68] N.
Cayley [Cayley 79] A.
Chan Chan et al. 13] M.
Coble [Coble 29] A.
Dolgachev [Dolgachev and Ortland 88] I.
Eisenbud [Eisenbud 05] D.
Eisenbud [Eisenbud 95] D.
Geck [Geck and Pfeiffer 00] M.
Glass [Glass 80] J. P.
Hermann [Hermann et al. 09] S.
Hudson Hudson 05] R.
Khaled [Khaled 95] A.
Kimura [Kimura 81] T.
Kondo [Kondo 11] S.
Runge [Runge 93] B.
Wirtinger Wirtinger 95] W.
Publication venue: 'Informa UK Limited'
Publication date: 01/01/2013
Field of study

The universal Kummer threefold is a 9-dimensional variety that represents the total space of the 6-dimensional family of Kummer threefolds in 7-dimensional projective space. We compute defining polynomials for three versions of this family, over the Satake hypersurface, over the G\"opel variety, and over the reflection representation of type E7. We develop classical themes such as theta functions and Coble's quartic hypersurface using current tools from combinatorics, geometry, and commutative algebra. Symbolic and numerical computations for genus 3 moduli spaces appear alongside toric and tropical methods.Comment: 50 pages; v2: added Remark 4.3, strengthened Lemma 8.3; v3: added references and added supplementary files to sourc

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Alshourbagy M (Alshourbagy, M.)[ 4 ]
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Avino S (Avino, S.)[ 7,2 ]
Babusci D (Babusci, D.)[ 8,11 ]
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Barsotti L (Barsotti, L.)[ 4 ]
Barsuglia M (Barsuglia, M.)[ 10 ]
Bauer TS (Bauer, T. S.)[ 4,13,14 ]
Beauville F (Beauville, F.)[ 11 ]
Bigotta S (Bigotta, S.)[ 4 ]
Birindelli S (Birindelli, S.)[ 4 ]
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Boccara C (Boccara, C.)[ 12 ]
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Brillet A (Brillet, A.)[ 6 ]
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Campagna E (Campagna, E.)[ 15,16,17 ]
Carbognani F (Carbognani, F.)[ 9 ]
Cavalier F (Cavalier, F.)[ 10 ]
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Chassande-Mottin E (Chassande-Mottin, E.)[ 6 ]
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del Prete M (del Prete, M.)[ 4 ]
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Puppo P (Puppo, P.)[ 5 ]
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Publication venue
Publication date: 01/01/2008
Field of study

Archivio della Ricerca - Università di Salerno