Smooth Compactifications of Locally Symmetric Varieties

Abstract

The new edition of this celebrated and long-unavailable book preserves the original book's content and structure and its unrivalled presentation of a universal method for the resolution of a class of singularities in algebraic geometry. At the same time, the book has been completely re-typeset, errors have been eliminated, proofs have been streamlined, the notation has been made consistent and uniform, an index has been added, and a guide to recent literature has been added. The book brings together ideas from algebraic geometry, differential geometry, representation theory and number theory, and will continue to prove of value for researchers and graduate students in these areas.

Siegel metric and curvature of the moduli space of curves

“…We recall that the image of the sectional curvature of H g is the segment [−1, − 1 g ] and that the tangent directions V such that H(V ) = −1 correspond to the symmetric matrices of rank 1.…”

Siegel Modular Forms and Their Applications

“…They depend on the choice of a certain cone decomposition of the cone of positive definite bilinear forms in g variables, cf. [7]. The 'boundary'à g − A g is a divisor with normal crossings and one has a universal semi-abelian variety overà g in the orbifold sense.…”

Kudla’s Modularity Conjecture and Formal Fourier–jacobi Series

“…We stress that Formal Fourier-Jacobi series no convergence assumption is required of such a series. For t ∈ Sym g (Q), we define the formal Fourier coefficients c( f, t) of f by means of the coefficients c(φ m ; n, r ) of the φ m and identity (3). We call f a symmetric formal FourierJacobi series (of weight k, genus g, and cogenus l) if its coefficients satisfy (4) for all u ∈ GL g (Z).…”