<p>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 \textit{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. </p>
| Identifer | oai:union.ndltd.org:purdue.edu/oai:figshare.com:article/22687264 |
| Date | 26 April 2023 |
| Creators | Hunter Simper (15347248) |
| Source Sets | Purdue University |
| Detected Language | English |
| Type | Text, Thesis |
| Rights | CC BY 4.0 |
| Relation | https://figshare.com/articles/thesis/Local_Cohomology_of_Determinantal_Thickening_and_Properties_of_Ideals_of_Minors_of_Generalized_Diagonal_Matrices_/22687264 |
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