Realizations of Polylogarithms

Classically, higher logarithms appear as multivalued fuction on the projective line. More recently they can be interpreted as entries of the period matrix of a certain variation of Hodge structure, itself called the "polylogarithm". Documenting the sheaf-theoretical foundations of the field of polylogarithms, this text assumes a sound background in algebraic geometry. Large parts of the text are intended as a reference for the working mathematician. Where a self-contained explanation was not possible, the author gives references in order to make the material accessible for advanced graduate students.