Singular Fano 4-folds

单一 Fano 4 折

• 批准号: 2737745
• 金额: --
• 依托单位: University of Warwick
• 依托单位国家: 英国
• 项目类别: Studentship
• 财政年份: 2022
• 资助国家: 英国
• 起止时间: 2022 至 无数据
• 项目状态: 未结题
• 来源: https://gtr.ukri.org/projects?ref=studentship-2737745
• 关键词: Singular; Fano; folds

Fano 3-folds have been studied for nearly a century, with the 1 and 2 dimensional cases being solved in the 19th century. There is no classification for Fano 3-folds, however it is known that they can be sorted into only finitely many deformation families. Notably, for some of the important classes classifications have been achieved. In particular, the "famous 95", the families whose general member is embedded pluri-anticanonically as a hypersurface.Birkar's celebrated theorem on the boundedness of Fano varieties proved that in any dimension, with very general hypotheses on the possible singularities, there are only finitely many deformation families for Fano varieties. Working with the terminal singularities of the standard minimal model program, we can ask to enumerate certain subclasses. In 4 dimensions, hypersurfaces that are quasismooth were classified in 2016. Unlike in 3 dimensions, however, there is no q-smoothing result for 4-folds, and the quasismooth case is not expected to account for the majority of hypersurfaces. The project will enumerate terminal Fano 4-folds that are not quasismooth giving the first indication of the weakness of the quasismooth assumption.

Fano 3-folds的研究已经有近世纪的历史，其中一维和二维的情况在世纪才得到解决。对于Fano 3-folds没有分类，但是已知它们可以被分类为仅100多个变形族。值得注意的是，一些重要的类别已经实现了分类。Birkar关于Fano簇的有界性的著名定理证明了在任何维数上，在对可能的奇点作非常一般的假设的情况下，Fano簇的变形族只有100多个。使用标准最小模型程序的终端奇点，我们可以要求枚举某些子类。在4维空间中，准光滑的超曲面在2016年被分类。然而，与3维不同的是，对于4重，没有q平滑的结果，并且准平滑的情况预计不会占大多数超曲面。该项目将列举终端法诺4倍，不准光滑给第一个迹象的弱点准光滑假设。