Title
Four dimensional symplectic geometry over the field with three elements and a moduli space of abelian surfaces
Document Type
Article
Publication Date
12-1-2001
Abstract
We study certain combinatorial structures related to the simple group of order 25920. Our viewpoint is to regard this group as G = PSp(4,F3), and so we describe these configurations in terms of the symplectic geometry of the four dimensional space over the field with three elements. Because of the isogeny between SO(5) and Sp(4) we can also describe these in terms of an inner product space of dimension five over that same field. The study of these configurations goes back to the 19th-century, and we relate our work to that of previous authors. We also discuss a more modern connection: these configurations arise in the theory of the Igusa compactification of the moduli space of principally polarized Abelian surfaces with a level three structure.
Publication Source (Journal or Book title)
Note di Matematica
First Page
111
Last Page
157
Recommended Citation
Hoffman, J., & Weintraub, S. (2001). Four dimensional symplectic geometry over the field with three elements and a moduli space of abelian surfaces. Note di Matematica, 20 (1), 111-157. Retrieved from https://repository.lsu.edu/mathematics_pubs/505