The Tits building of Siegel modular groups of genus 2 (Q5956162)

The aim of the present paper is to study the Tits buildings associated to certain Siegel modular groups. The Siegel modular groups considered here correspond to the moduli spaces of certain abelian varieties with level structure, and their associated Tits buildings give then the configuration of the boundary components in the compactified moduli spaces. This means that the explicit description of the according Tits buildings (for the particular Siegel modular groups \(\widetilde{\Gamma}_{1,t}^0\) and \(\widetilde{\Gamma}_{1,t}\) considered here, with \(t\) being a square-free number) provides some valuable geometric information about some special compactified moduli spaces of abelian varieties in algebraic geometry. The various Tits buildings are explicitly described by rather elementary, but very subtle and naturally tedious computations. However, the results are beautiful, important and enlightening. Colour pictures that illustrate nicely the geometric content of the results are available from the internet at \url{http://www.bath.ac.uk/~masgks/Buildings}, and these pictures provide a rich compensation for the lengthy computations leading to them.