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Title:The Behavior on the Restriction of Divisor Classes to Sequences of Hypersurfaces
Author(s):Spiroff, Sandra Marie
Doctoral Committee Chair(s):Griffith, Phillip A.
Department / Program:Mathematics
Discipline:Mathematics
Degree Granting Institution:University of Illinois at Urbana-Champaign
Degree:Ph.D.
Genre:Dissertation
Subject(s):Mathematics
Abstract:Let A be an excellent local normal domain and fninfinity n=1 a sequence of prime elements lying in successively higher powers of the maximal ideal, such that each hypersurface A/ fnA satisfies R1. We establish the map of divisor classes jn*: Cl(A) → Cl((A/fnA)'), where (A/fnA)' represents the integral closure, and investigate the injectivity of jn*. The first result shows that no nontrivial divisor class can lie in every kernel. Secondly, when A is an isolated singularity containing a field of characteristic zero, dim A ≥ 4, and A has a small Cohen-Macaulay module, then we show that there is an integer N > 0 such that fn ∈ mN ⇒ jn* is injective. We substantiate these results with a general construction that provides a large collection of examples.
Issue Date:2003
Type:Text
Language:English
Description:40 p.
Thesis (Ph.D.)--University of Illinois at Urbana-Champaign, 2003.
URI:http://hdl.handle.net/2142/86823
Other Identifier(s):(MiAaPQ)AAI3101974
Date Available in IDEALS:2015-09-28
Date Deposited:2003


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