The universal Kummer threefold

Qingchun Ren, Steven V. Sam, Gus Schrader, Bernd Sturmfels

Research output: Contribution to journalArticlepeer-review

16 Scopus citations


The universal Kummer threefold is a 9-dimensional variety that represents the total space of the 6-dimensional family of Kummer threefolds in P7. We compute defining polynomials for three versions of this family, over the Satake hypersurface, over the Göpel variety, and over the reflection representation of type E7. We develop classical themes such as theta functions and Coble's quartic hypersurfaces using current tools from combinatorics, geometry, and commutative algebra. Symbolic and numerical computations for genus-3 moduli spaces appear alongside toric and tropical methods.

Original languageEnglish (US)
Pages (from-to)327-362
Number of pages36
JournalExperimental Mathematics
Issue number3
StatePublished - 2013
Externally publishedYes


  • Abelian varieties
  • Moduli spaces
  • Theta functions
  • Toric varieties

ASJC Scopus subject areas

  • General Mathematics


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