Toroidal Compactifications and Dimension Formulas for Spaces of Modular Forms for Orthogonal Shimura Varieties

Andrew Fiori

Published 2016-10-16Version 1

In this paper we describe the general theory of constructing toroidal compactifications of locally symmetric spaces and using these to compute dimension formulas for spaces of modular forms. We focus explicitly on the case of the orthogonal locally symmetric spaces arising from quadratic forms of signature $(2,n)$, giving explicit details of the constructions, structures and results in these cases. This article does not give explicit cone decompositions, compute explicit intersection pairings, or count cusps and thus does not give any complete formulas for the dimensions. This article is still `in preparation'.