<p>The family of algebraic surfaces X defined by the single equation [special characters omitted] over an algebraically closed field <i>k</i> of characteristic zero, where a<sub>1</sub>, …, a<sub>n</sub> are distinct, is studied. It is shown that this is a rational surface with a non-rational singularity at the origin. The ideal class group of the surface is computed. The terms of the Chase-Harrison-Rosenberg seven term exact sequence on the open complement of the ramification locus of <i>X</i>→[special characters omitted] are computed; the Brauer group is also studied in this unramified setting.</p><p> The analysis is extended to the surface <i>X˜</i> obtained by blowing up <i>X</i> at the origin. The interplay between properties of <i>X˜</i> , determined in part by the exceptional curve <i> E</i> lying over the origin, and the properties of <i>X</i> is explored. In particular, the implications that these properties have on the Picard group of the surface <i>X</i> are studied.</p>
| Identifer | oai:union.ndltd.org:PROQUEST/oai:pqdtoai.proquest.com:3571442 |
| Date | 28 August 2013 |
| Creators | Harmon, Drake |
| Publisher | Florida Atlantic University |
| Source Sets | ProQuest.com |
| Language | English |
| Detected Language | English |
| Type | thesis |
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