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Title

A class of rational surfaces with a nonrational singularity explicitly given by a single equation.

Creator

Harmon, Drake., Charles E. Schmidt College of Science, Department of Mathematical Sciences

Abstract/Description

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...
Show moreThe 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.
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Date Issued

2013

PURL

http://purl.flvc.org/fcla/dt/3360782

Subject Headings

Mathematics, Galois modules (Algebra), Class field theory, Algebraic varieties, Integral equations

Format

Document (PDF)