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class of rational surfaces with a nonrational singularity explicitly given by a single equation
 Date Issued:
 2013
 Summary:
 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 nonrational singularity at the origin. The ideal class group of the surface is computed. The terms of the ChaseHarrisonRosenberg 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.
Title:  A class of rational surfaces with a nonrational singularity explicitly given by a single equation. 
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Name(s): 
Harmon, Drake. Charles E. Schmidt College of Science Department of Mathematical Sciences 

Type of Resource:  text  
Genre:  Electronic Thesis Or Dissertation  
Date Issued:  2013  
Publisher:  Florida Atlantic University  
Physical Form:  electronic  
Extent:  viii, 75 p. : ill.  
Language(s):  English  
Summary:  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 nonrational singularity at the origin. The ideal class group of the surface is computed. The terms of the ChaseHarrisonRosenberg 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.  
Identifier:  851066719 (oclc), 3360782 (digitool), FADT3360782 (IID), fau:4094 (fedora)  
Note(s): 
by Drake Harmon. Vita. Thesis (Ph.D.)Florida Atlantic University, 2013. Includes bibliography. Mode of access: World Wide Web. System requirements: Adobe Reader. 

Subject(s): 
Mathematics Galois modules (Algebra) Class field theory Algebraic varieties Integral equations 

Persistent Link to This Record:  http://purl.flvc.org/fcla/dt/3360782  
Use and Reproduction:  http://rightsstatements.org/vocab/InC/1.0/  
Owner Institution:  FAU 