Quantum multiplicative hypertoric varieties and localization
<p>In this thesis, we consider <em>q</em>-deformations of multiplicative Hypertoric varieties, where <em>q</em>∈&Kopf;<sup>x</sup> for &Kopf; an algebraically closed field of characteristic 0. We construct an algebra 𝒟<sub>q</sub>...
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| Format: | Thesis |
| Language: | English |
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2014
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| _version_ | 1797055752474460160 |
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| author | Cooney, N |
| author2 | Kremnitzer, Y |
| author_facet | Kremnitzer, Y Cooney, N |
| author_sort | Cooney, N |
| collection | OXFORD |
| description | <p>In this thesis, we consider <em>q</em>-deformations of multiplicative Hypertoric varieties, where <em>q</em>∈&Kopf;<sup>x</sup> for &Kopf; an algebraically closed field of characteristic 0. We construct an algebra 𝒟<sub>q</sub> of <em>q</em>-difference operators as a Heisenberg double in a braided monoidal category. We then focus on the case where <em>q</em> is specialized to a root of unity. In this setting, we use 𝒟<sub>q</sub> to construct an Azumaya algebra on an <em>l</em>-twist of the multiplicative Hypertoric variety, before showing that this algebra splits over the fibers of both the moment and resolution maps. Finally, we sketch a derived localization theorem for these Azumaya algebras. </p> |
| first_indexed | 2024-03-06T19:14:17Z |
| format | Thesis |
| id | oxford-uuid:17d0824f-e8f2-4cb7-9e84-dd3850a9e2a2 |
| institution | University of Oxford |
| language | English |
| last_indexed | 2024-03-06T19:14:17Z |
| publishDate | 2014 |
| record_format | dspace |
| spelling | oxford-uuid:17d0824f-e8f2-4cb7-9e84-dd3850a9e2a22022-03-26T10:39:41ZQuantum multiplicative hypertoric varieties and localizationThesishttp://purl.org/coar/resource_type/c_db06uuid:17d0824f-e8f2-4cb7-9e84-dd3850a9e2a2Algebraic geometryMathematicsGroup theory and generalizations (mathematics)EnglishOxford University Research Archive - Valet2014Cooney, NKremnitzer, Y<p>In this thesis, we consider <em>q</em>-deformations of multiplicative Hypertoric varieties, where <em>q</em>∈&Kopf;<sup>x</sup> for &Kopf; an algebraically closed field of characteristic 0. We construct an algebra 𝒟<sub>q</sub> of <em>q</em>-difference operators as a Heisenberg double in a braided monoidal category. We then focus on the case where <em>q</em> is specialized to a root of unity. In this setting, we use 𝒟<sub>q</sub> to construct an Azumaya algebra on an <em>l</em>-twist of the multiplicative Hypertoric variety, before showing that this algebra splits over the fibers of both the moment and resolution maps. Finally, we sketch a derived localization theorem for these Azumaya algebras. </p> |
| spellingShingle | Algebraic geometry Mathematics Group theory and generalizations (mathematics) Cooney, N Quantum multiplicative hypertoric varieties and localization |
| title | Quantum multiplicative hypertoric varieties and localization |
| title_full | Quantum multiplicative hypertoric varieties and localization |
| title_fullStr | Quantum multiplicative hypertoric varieties and localization |
| title_full_unstemmed | Quantum multiplicative hypertoric varieties and localization |
| title_short | Quantum multiplicative hypertoric varieties and localization |
| title_sort | quantum multiplicative hypertoric varieties and localization |
| topic | Algebraic geometry Mathematics Group theory and generalizations (mathematics) |
| work_keys_str_mv | AT cooneyn quantummultiplicativehypertoricvarietiesandlocalization |