The family of algebraic surfaces X defined by the single equation [special characters omitted] over an algebraically closed field k of characteristic zero, where a1, …, an 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 X→[special characters omitted] are computed; the Brauer group is also studied in this unramified setting.
The analysis is extended to the surface X˜ obtained by blowing up X at the origin. The interplay between properties of X˜ , determined in part by the exceptional curve E lying over the origin, and the properties of X is explored. In particular, the implications that these properties have on the Picard group of the surface X are studied.
|Advisor:||Ford, Timothy J.|
|Commitee:||Klinger, Lee, Steinwandt, Rainer, Wang, Yuan|
|School:||Florida Atlantic University|
|School Location:||United States -- Florida|
|Source:||DAI-B 74/11(E), Dissertation Abstracts International|
|Subjects:||Mathematics, Theoretical Mathematics|
|Keywords:||Algebraic geometry, Birational geometry, Brauer groups, Divisors, Non-rational singularity, Ring theory, Singularity explicitly|
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