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class of rational surfaces with a non-rational 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 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.
Title: | A class of rational surfaces with a non-rational 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 |
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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 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. | |
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. |
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Subject(s): |
Mathematics Galois modules (Algebra) Class field theory Algebraic varieties Integral equations |
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Persistent Link to This Record: | http://purl.flvc.org/fcla/dt/3360782 | |
Use and Reproduction: | http://rightsstatements.org/vocab/InC/1.0/ | |
Host Institution: | FAU |