Dissertation/Thesis Abstract

A class of rational surfaces with a non-rational singularity explicitly given by a single equation
by Harmon, Drake, Ph.D., Florida Atlantic University, 2013, 84; 3571442
Abstract (Summary)

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 obtained by blowing up X at the origin. The interplay between properties of , 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.

Indexing (document details)
Advisor: Ford, Timothy J.
Commitee: Klinger, Lee, Steinwandt, Rainer, Wang, Yuan
School: Florida Atlantic University
Department: Mathematical Sciences
School Location: United States -- Florida
Source: DAI-B 74/11(E), Dissertation Abstracts International
Source Type: DISSERTATION
Subjects: Mathematics, Theoretical Mathematics
Keywords: Algebraic geometry, Birational geometry, Brauer groups, Divisors, Non-rational singularity, Ring theory, Singularity explicitly
Publication Number: 3571442
ISBN: 9781303228193
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