The goal of this thesis is to study Rees algebra R(I) and the special fiber ring F(I) for a family of ideals. Given a map between projective spaces parameterizing a variety, the Rees algebra is the coordinate ring of the graph and the special fiber ring is the coordinate ring of the image. We will compute the defining ideal of these algebras. Let R=k[x_1, …, x_d] for d greater than or equal to 4 be a polynomial ring with homogeneous maximal ideal m. We study the Rideals I which are mprimary, Gorenstein, generated in degree 2, and have a Gorenstein linear resolution. The defining ideal of the Rees algebra will be of fiber type. That is, the defining ideal of the Rees algebra is generated by the defining ideals of the special fiber ring and of the symmetric algebra. The defining ideal of the symmetric algebra is well understood, so we concentrate on computing the defining ideal of the special fiber ring. In Chapter 4, the defining ideal of the special fiber ring F(I) will be given as a subideal of the 2x2 minors of a symmetric matrix of variables modeled after the defining ideal of F(m^2). In Chapter 5, the defining ideal of the special fiber ring of I will be described as a saturation of the maximal minors of the Jacobian dual. We include both descriptions of the defining ideal in this manuscript because while the methods in Chapter 4 give explicit polynomial generators of the defining ideal, the methods in Chapter 5 are more likely to generalize to the larger class of mprimary Gorenstein ideals having a Gorenstein linear resolution.
On the Coordinate Ring of a Projection of a Degree Two Veronese Variety
Doctoral Dissertation
Abstract
Attribute Name  Values 

Author  Whitney Liske 
Contributor  Claudiu Raicu, Committee Member 
Contributor  Claudia Polini, Research Director 
Contributor  Alessio Sammartano, Committee Member 
Contributor  Juan Migliore, Committee Member 
Degree Level  Doctoral Dissertation 
Degree Discipline  Mathematics 
Degree Name  Doctor of Philosophy 
Banner Code 

Defense Date 

Submission Date  20190405 
Record Visibility  Public 
Content License  
Departments and Units  
Catalog Record 
Digital Object Identifier
This DOI is the best way to cite this doctoral dissertation.
Files
Thumbnail  File Name  Description  Size  Type  File Access  Actions 

LiskeW042019D.pdf  589 KB  application/pdf  Public 
1 entry found