Abelian varieties and their moduli are a central topic of increasing importance in today`s mathematics. Applications range from algebraic geometry and number theory to mathematical physics.
The present collection of 17 refereed articles originates from the third "Texel Conference" held in 1999. Leading experts discuss and study the structure of the moduli spaces of abelian varieties and related spaces, giving an excellent view of the state of the art in this field.
The book will appeal to pure mathematicians, especially algebraic geometers and number theorists, but will also be relevant for researchers in mathematical physics.
On extra components in the functorial compactification of Ag.- On Mumford's uniformization and Néron models of Jacobians of semistable curves over complete rings.- Torelli theorem via Fourier-Mukai transform.- On the André-Oort conjecture for Hilbert modular surfaces.- Toroidal resolutions for some matrix singularities.- Formal Brauer groups and moduli of abelian surfaces.- Isogeny classes of abelian varieties with no principal polarizations.- Igusa's modular form and the classification of Siegel modular threefolds.- Mirror symmetry and quantization of abelian varieties.- Group schemes with additional structures and Weyl group cosets.- Moduli space of elliptic curves with Heisenberg level structure.- Singularities of the height strata in the moduli of K3 surfaces.- A stratification of a moduli space of abelian varieties.- Newton polygon strata in the moduli space of abelian varieties.- The dimension of Oort strata of Shimura varieties of PEL-type.- Hyperelliptic Jacobians and modular representations.- Windows for displays of p-divisible groups.
