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Faithful tropicalization of hypertoric varietiesKutler, Max 06 September 2017 (has links)
The hypertoric variety M_A defined by an arrangement A of affine hyperplanes admits a natural tropicalization, induced by its embedding in a Lawrence toric variety. In this thesis, we explicitly describe the polyhedral structure of this tropicalization and calculate the fibers of the tropicalization map. Using a recent result of Gubler, Rabinoff, and Werner, we prove that there is a continuous section of the tropicalization map.
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GKZ Hypergeometric Systems and Projective Modules in Hypertoric Category OHilburn, Justin 27 October 2016 (has links)
In this thesis I show that indecomposable projective and tilting modules in hypertoric category O are obtained by applying a variant of the geometric Jacquet functor of Emerton, Nadler, and Vilonen to certain Gel'fand-Kapranov-Zelevinsky hypergeometric systems. This proves the abelian case of a conjecture of Bullimore, Gaiotto, Dimofte, and Hilburn on the behavior of generic Dirichlet boundary conditions in 3d N=4 SUSY gauge theories.
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On an algebro-geometric realization of the cohomology ring of conical symplectic resolutions / 錐的シンプレクティック特異点解消のコホモロジー環の代数幾何学的実現についてHikita, Tatsuyuki 25 May 2015 (has links)
京都大学 / 0048 / 新制・課程博士 / 博士(理学) / 甲第19166号 / 理博第4106号 / 新制||理||1591(附属図書館) / 32158 / 京都大学大学院理学研究科数学・数理解析専攻 / (主査)准教授 加藤 周, 教授 並河 良典, 教授 雪江 明彦 / 学位規則第4条第1項該当 / Doctor of Science / Kyoto University / DFAM
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The universal covers of hypertoric varieties and Bogomolov’s decomposition / 超トーリック多様体の普遍被覆とボゴモロフ分解Nagaoka, Takahiro 23 March 2022 (has links)
京都大学 / 新制・課程博士 / 博士(理学) / 甲第23686号 / 理博第4776号 / 新制||理||1684(附属図書館) / 京都大学大学院理学研究科数学・数理解析専攻 / (主査)教授 並河 良典, 教授 玉川 安騎男, 教授 望月 拓郎 / 学位規則第4条第1項該当 / Doctor of Science / Kyoto University / DFAM
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