Moduli of Supersingular Abelian Varieties Abelian varieties can be classified via their moduli. In positive characteristic the structure of the p torsion structure is an additional useful tool. For that structure supersingular abelian varieties can be considered the most special ones. They provide a starting point for the fine description of various structures. For low dimensions the moduli of supersingular abelian varieties is by now well understood. In this book we provide a description of the supersingular locus in all dimensions in particular we compute the dimension of it: it turns out to be equal to Äg.g 4Ü and we express the number of components as a class number thus completing a long historical line where special cases were studied and general results were conjectured (Deuring Hasse Igusa Oda Oort Katsura Oort)