Zariski-Kammern und stabile Basisorte auf Del-Pezzo- und K3-Flächen

Zariski-Kammern liefern eine Zerlegung des Big-Kegels einer glatten projektiven Fläche in rationale lokal polyedrische Teilkegel mit interessanten Eigenschaften aus der Sicht von Linearsystemen: Im Inneren jedes Teilkegels ist der stabile Basisort konstant und die Volumenfunktion ist in jedem Teilke...

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Bibliographic Details
Main Author: Funke, Michael
Contributors: Bauer, Thomas (Prof. Dr.) (Thesis advisor)
Format: Doctoral Thesis
Published: Philipps-Universität Marburg 2009
Online Access:PDF Full Text
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Table of Contents: Zariski chambers provide a natural decomposition of the big cone of a smooth projective surface into rational locally polyhedral subcones that are interesting from the point of view of linear series: in the interior of each of the subcones the stable base loci are constant and on each subcone the volume function is given by a single polynomial of degree two. This thesis deals with Zariski chambers on Del Pezzo and K3 surfaces. The aspect of counting Zariski chambers is discussed with the example of Del Pezzo surfaces. The decomposition of the big cone in Zariski chambers is compared – especially for K3 surfaces – with the decomposition in Weyl chambers. The mutual inclusions of Zariski and Weyl chambers on K3 surfaces are described in detail. Finally, there is a detailed research on the local geometry of Zariski chambers on Kummer surfaces.