Diploma Thesis
Lars Petersen
Classification of line bundles over hyperelliptic curves
From 1 Mar 2005 to 1 Nov 2005
Advisor: PD Dr. Georg Hein
We describe the Picard group of a hyperelliptic curve using explicit methods from commutative algebra. Considering a free rank two module over a Euclidean ring we provide this module with an algebra structure by choosing a suitable element of the ring. Thus we are able to study line bundles on an affine hyperelliptic curve via examining "standard forms" of 2x2 matrices over this algebra. The affine framework is later on used to get the global picture in the case of a projective curve.
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