40 research outputs found
The Universal Kummer Threefold
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
Multicoloured Random Graphs: Constructions and Symmetry
This is a research monograph on constructions of and group actions on
countable homogeneous graphs, concentrating particularly on the simple random
graph and its edge-coloured variants. We study various aspects of the graphs,
but the emphasis is on understanding those groups that are supported by these
graphs together with links with other structures such as lattices, topologies
and filters, rings and algebras, metric spaces, sets and models, Moufang loops
and monoids. The large amount of background material included serves as an
introduction to the theories that are used to produce the new results. The
large number of references should help in making this a resource for anyone
interested in beginning research in this or allied fields.Comment: Index added in v2. This is the first of 3 documents; the other 2 will
appear in physic
Collection of abstracts of the 24th European Workshop on Computational Geometry
International audienceThe 24th European Workshop on Computational Geomety (EuroCG'08) was held at INRIA Nancy - Grand Est & LORIA on March 18-20, 2008. The present collection of abstracts contains the 63 scientific contributions as well as three invited talks presented at the workshop
LIPIcs, Volume 261, ICALP 2023, Complete Volume
LIPIcs, Volume 261, ICALP 2023, Complete Volum
LIPIcs, Volume 244, ESA 2022, Complete Volume
LIPIcs, Volume 244, ESA 2022, Complete Volum