Titel: Explicit methods for hyperelliptic curves and the Kummer variety - The genus 4 case

Zusammenfassung:
Hyperelliptic curves, i.e. curves defined by a polynomial equation of the form y^2 = F(x), have a fairly well understood theoretical description. If we want to do computations for any given curve however - like finding rationals points on it or finding generators of the Mordell-Weil group - we need some explicit description. Based on work by Michael Stoll we approach the situation of genus 4. We give as best as possible an explicit description of the Jacobian and its group structure and explain how and why the Kummer variety helps. As a possible application we look into the theory of height functions.