The Behavior on the Restriction of Divisor Classes to Sequences of Hypersurfaces
Spiroff, Sandra Marie
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https://hdl.handle.net/2142/86823
Description
Title
The Behavior on the Restriction of Divisor Classes to Sequences of Hypersurfaces
Author(s)
Spiroff, Sandra Marie
Issue Date
2003
Doctoral Committee Chair(s)
Griffith, Phillip A.
Department of Study
Mathematics
Discipline
Mathematics
Degree Granting Institution
University of Illinois at Urbana-Champaign
Degree Name
Ph.D.
Degree Level
Dissertation
Keyword(s)
Mathematics
Language
eng
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.
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