University of Illinois Urbana-Champaign

Hypersurface Sections: A Study of Divisor Class Groups and of the Complexity of Tensor Products

Miller, Claudia Maria

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Description

Title
Hypersurface Sections: A Study of Divisor Class Groups and of the Complexity of Tensor Products
Author(s)
Miller, Claudia Maria
Issue Date
1997
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
The second part concerns the notion of complexity, a measure of the growth of the Betti numbers of a module. We show that over a complete intersection R the complexity of the tensor product $M\otimes\sb{R}N$ of two finitely generated modules is the sum of the complexities of each if $Tor\sbsp{i}{R}(M,\ N)=0$ for $i\ge1.$ One of the applications is simplification of the proofs of central results over hypersurface rings in a paper of C. Huneke and R. Wiegand on the tensor product of modules and the rigidity of Tor (HW1).
Graduation Semester
1997
Type of Resource
text
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