On the Nash Problem over 3-Fold Terminal Singularities
| dc.contributor.advisor | Docampo Álvarez, Roi | |
| dc.contributor.author | Lin, Steven | |
| dc.contributor.committeeMember | Maher, Erin | |
| dc.contributor.committeeMember | Mandel, Travis | |
| dc.contributor.committeeMember | Muller, Gregory | |
| dc.contributor.committeeMember | Özaydın, Murad | |
| dc.date.accessioned | 2025-08-05T19:08:18Z | |
| dc.date.embargoExpiration | ||
| dc.date.issued | 2025 | |
| dc.date.proquestAvailable | 01/01/2025 | |
| dc.date.updated | 2025-08-05T19:08:18Z | |
| dc.description.abstract | In this dissertation, we study the Nash problem over terminal singularities in dimension 3, or 3-fold terminal singularities. In particular, for 3-fold terminal singularities, we propose two conjectures that aim to characterize their induced Nash valuations. (A) Any prime divisor with discrepancy bounded by 1 induces a Nash valuation. (B) Any prime divisor with minimal discrepancy induces a Nash valuation. We prove that Conjecture A holds for toric terminal singularities in arbitrary dimension, and Conjecture B holds for 3-fold terminal singularities of type cAx/2. In the Gorenstein cases, we provide a partial result with examples for both of the conjectures. | |
| dc.identifier.orcid | 0009-0005-8615-3036 | |
| dc.identifier.uri | https://shareok.org//handle/11244/341608 | |
| dc.language.iso | en | |
| dc.publisher | University of Oklahoma – Graduate College | |
| dc.subject | Mathematics | |
| dc.subject | Arc Space | |
| dc.subject | Divisorial Contraction with Minimal Discrepancy | |
| dc.subject | Nash Valuation | |
| dc.subject | Resolution of Singularities | |
| dc.subject | Terminal Singularity | |
| dc.subject | Toric Variety | |
| dc.thesis.degree | D.Phil. | |
| dc.title | On the Nash Problem over 3-Fold Terminal Singularities | |
| ou.group | Mathematics: Arts & Sciences |