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1	Faithful tropicalization of hypertoric varieties Kutler, 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. Hypertoric varieties Matroids Non-Archimedean Geometry Tropical geometry
2	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 hypertoric varieties conical symplectic varieties universal cover fundamental group of regular locus Bogomolov's decomposition uniqueness of symplectic structure 400