F-purity of Hypersurfaces.
dc.contributor.author | Hernandez, Daniel Jesus | en_US |
dc.date.accessioned | 2011-09-15T17:17:08Z | |
dc.date.available | NO_RESTRICTION | en_US |
dc.date.available | 2011-09-15T17:17:08Z | |
dc.date.issued | 2011 | en_US |
dc.date.submitted | en_US | |
dc.identifier.uri | https://hdl.handle.net/2027.42/86491 | |
dc.description.abstract | Recent work of Hara and Watanabe extends the classical and much-studied notion of F-purity for rings of prime characteristic to the setting of pairs. We study the condition of F-purity for hypersurfaces (i.e., principal ideals) in F-pure rings. In particular, much of this thesis is dedicated to the study of F-pure thresholds, and we are strongly motivated by the connection between F-purity (defined via the Frobenius morphism) and log canonical singularities (defined via resolution of singularities) . We deduce some important properties of F-purity and F-pure thresholds, and use them to show that log canonical singularities is equivalent to dense F-pure type for very general hypersurfaces in complex affine space. We also give algorithms for computing the F-pure threshold of an arbitrary diagonal or binomial hypersurface. In the diagonal case, we compute the first non-trivial test ideal of the pair, as well as some higher jumping numbers. | en_US |
dc.language.iso | en_US | en_US |
dc.subject | F-purity | en_US |
dc.subject | F-pure Threshold | en_US |
dc.subject | Frobenius Morphism | en_US |
dc.title | F-purity of Hypersurfaces. | en_US |
dc.type | Thesis | en_US |
dc.description.thesisdegreename | PhD | en_US |
dc.description.thesisdegreediscipline | Mathematics | en_US |
dc.description.thesisdegreegrantor | University of Michigan, Horace H. Rackham School of Graduate Studies | en_US |
dc.contributor.committeemember | Smith, Karen E. | en_US |
dc.contributor.committeemember | Hochster, Melvin | en_US |
dc.contributor.committeemember | Meadows, Guy A. | en_US |
dc.contributor.committeemember | Mustata, Mircea Immanuel | en_US |
dc.contributor.committeemember | Zhang, Wenliang | en_US |
dc.subject.hlbsecondlevel | Mathematics | en_US |
dc.subject.hlbtoplevel | Science | en_US |
dc.description.bitstreamurl | http://deepblue.lib.umich.edu/bitstream/2027.42/86491/1/dhernan_1.pdf | |
dc.owningcollname | Dissertations and Theses (Ph.D. and Master's) |
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