A survey on the conjecturally minimal volume of klt ample (resp. Fano) varieties and specific classification of 3-folds canonical thresholds in the open interval (1/3,1/2)

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题名:	A survey on the conjecturally minimal volume of klt ample (resp. Fano) varieties and specific classification of 3-folds canonical thresholds in the open interval (1/3,1/2)
作者:	吳宏宜;Wu, Hung-Yi
贡献者:	數學系
关键词:	代數幾何;Algebraic geometry
日期:	2023-07-27
上传时间:	2024-09-19 17:20:34 (UTC+8)
出版者:	國立中央大學
摘要:	這篇碩士論文主要分為兩個部分，前半部分為整理Totaro的文章，將作者沒有闡述清楚的細節補齊，用一些更為淺顯易懂的敘述方式讓它更好閱讀。後半段則是從Totaro計算global log canonical threshold (glct)的地方出發，提出了一些相關問題，如：log canonical threshold (lct)及canonical threshold (ct)的計算。由於lct的計算相對發展的完全，我們選擇了去研究ct的樣貌，此部分的主要結果為：刻畫三維光滑的代數簇在(1/3,1/2)開區間中所有會發生的ct。;This thesis is mainly divided into two parts. The first half is to sort out Totaro′s paper, fill in the details that the author did not explain clearly, and use some methods to make it easier to read. The second half starts from Totaro′s calculations on the global log canonical threshold (glct) to ask some related issues, such as: the calculations of log canonical threshold (lct) and canonical threshold (ct). Since the calculations of lct are relatively developed, we choose to compute the ct in dimension 3. Finally, we describe completely the set of all values of ct in the smooth algebraic varieties in the open interval (1/3,1/2).
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