The Universal Kummer Threefold
Algebraic Geometry
2016-11-14 v3
Abstract
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.
Cite
@article{arxiv.1208.1229,
title = {The Universal Kummer Threefold},
author = {Qingchun Ren and Steven V Sam and Gus Schrader and Bernd Sturmfels},
journal= {arXiv preprint arXiv:1208.1229},
year = {2016}
}
Comments
50 pages; v2: added Remark 4.3, strengthened Lemma 8.3; v3: added references and added supplementary files to source