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A class of rational surfaces with a non-rational singularity explicitly given by a single equation

The family of algebraic surfaces X dened by the single equation zn = (y a1x) (y anx)(x 1) over an algebraically closed eld k of characteristic zero, where a1; : : : ; an 2 k 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 ramication locus of X ! A2 are computed; the Brauer group is also studied in this unramied setting. The analysis is extended to the surface eX obtained by blowing up X at the origin. The interplay between properties of eX , 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. / by Drake Harmon. / Vita. / Thesis (Ph.D.)--Florida Atlantic University, 2013. / Includes bibliography. / Mode of access: World Wide Web. / System requirements: Adobe Reader.

Identiferoai:union.ndltd.org:fau.edu/oai:fau.digital.flvc.org:fau_4094
ContributorsHarmon, Drake., Charles E. Schmidt College of Science, Department of Mathematical Sciences
PublisherFlorida Atlantic University
Source SetsFlorida Atlantic University
LanguageEnglish
Detected LanguageEnglish
TypeText, Electronic Thesis or Dissertation
Formatviii, 75 p. : ill., electronic
Rightshttp://rightsstatements.org/vocab/InC/1.0/

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