The Kodaira dimension of Siegel modular varieties of genus 3 or higher [Elektronische Ressource] / von Eric Schellhammer

The Kodaira dimension ofSiegel modular varieties of genus 3or higherVom Fachbereich Mathematik der Universitat¨ Hannoverzur Erlangung des GradesDoktor der NaturwissenschaftenDr. rer. nat.genehmigte DissertationvonDipl.-Math. Eric Schellhammergeboren am 18. November 1973 in Stuttgart2004schell@dbs.uni-hannover.deUniversitat¨ Hannover – Fachbereich MathematikFebruary 25, 2004Referent: Prof. Dr. Klaus Hulek, Universitat¨ HannoverKoreferent: Prof. Dr. Herbert Lange, Universitat¨ ErlangenTag der Promotion: 6. Februar 20042AbstractAn Abelian variety is a g-dimensional complex torus which is a projective variety. Inorder to obtain an embedding into projective space one has to chose an ample linebundle. To each such line bundle one can associate a polarisation which only dependson the class of the line bundle in the Neron-Se´ veri group. The type of the polarisation isgiven by a g-tuple of integers e ;:::;e with the property that eje for i = 1;:::;g 1.1 g i i+1ei+1If e = = e = 1, the polarisation is said to be principal. If the values are1 g eipairwise coprime, the is said to be coprime. Furthermore, we can givea symplectic basis for the group of n-torsion points, which is then called a level-nstructure.Not only Abelian varieties but also their moduli spaces have been of interest formany years.