Relative reduction numbers, regularity of blowup algebras, and Ulrich modules
We prove new results concerning the connection between (relative) reduction numbers and the Castelnuovo-Mumford regularity of blowup algebras and blowup modules. A key basic tool is the operation of (relative) Ratliff-Rush closure. First, we answer in two particular cases a question of M. E. Rossi,...
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| Format: | doctoral thesis |
| Status: | Published version |
| Publication Date: | 2022 |
| Country: | Brasil |
| Institution: | Universidade Federal da Paraíba (UFPB) |
| Repository: | Biblioteca Digital de Teses e Dissertações da UFPB |
| Language: | Portuguese |
| OAI Identifier: | oai:repositorio.ufpb.br:123456789/23449 |
| Online Access: | https://repositorio.ufpb.br/jspui/handle/123456789/23449 |
| Access Level: | Open access |
| Keyword: | Regularidade de Castelnuovo-Mumford Número de redução Álgebra de blowup Fecho de Ratliff-Rush Ideais e módulos de Ulrich generalizados Castelnuovo-Mumford regularity Reduction number Blowup algebra Ratliff-Rush closure Generalized Ulrich ideals and modules CNPQ::CIENCIAS EXATAS E DA TERRA::MATEMATICA |
| Summary: | We prove new results concerning the connection between (relative) reduction numbers and the Castelnuovo-Mumford regularity of blowup algebras and blowup modules. A key basic tool is the operation of (relative) Ratliff-Rush closure. First, we answer in two particular cases a question of M. E. Rossi, D. T. Trung, and N. V. Trung about Rees algebras of ideals in two-dimensional Buchsbaum local rings, and we even ask whether one of such situations always holds. In another theorem we generalize a result of A. Mafi on ideals in two-dimensional Cohen-Macaulay local rings, by extending it to arbitrary dimension and allowing for the setting relative to a Cohen-Macaulay module. We derive a number of applications, including progress on the theory of generalized Ulrich ideals and modules and improvements of results by other authors. |
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