Local Cohomology of Determinantal Thickening and Properties of Ideals of Minors of Generalized Diagonal Matrices
Abstract
This thesis is focused on determinantal rings in 2 different contexts. In Chapter 3 the homological properties of powers of determinantal ideals are studied. In particular the focus is on local cohomology of determinantal thickenings and we explicitly describe the R-module structure of some of these local cohomology modules. In Chapter 4 we introduce generalized diagonal matrices, a class of sparse matrices which contain diagonal and upper triangular matrices. We study the ideals of minors of such matrices and describe their properties such as height, multiplicity, and Cohen-Macaulayness.
Degree
Ph.D.
Advisors
Walther, Purdue University.
Subject Area
Mathematics
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