Applications of Frobenius splitting to algebraic geometry

Frobenius 分裂在代数几何中的应用

• 批准号: 23740024
• 负责人: TAKAGI Shunsuke
• 金额: $ 2.83万
• 依托单位: The University of Tokyo
• 依托单位国家: 日本
• 项目类别: Grant-in-Aid for Young Scientists (B)
• 财政年份: 2011
• 资助国家: 日本
• 起止时间: 2011 至 2013
• 项目状态: 已结题
• 来源: https://kaken.nii.ac.jp/grant/KAKENHI-PROJECT-23740024/
• 关键词: 可換環論; 代数幾何学; フロベニウス分裂; F特異点; Calabi-Yau多様体; F純特異点; 対数的標準特異点; 特異点; ファノ多様体; 可換環論; 代数幾何学; フロベニウス分裂; F特異点; Calabi-Yau多様体; F純特異点; 対数的標準特異点; 特異点; ファノ多様体

The goal of this research project was to give an affirmative answer to Schwede-Smith's conjecture, which says that a projective variety X over an algebraically closed field of characteristic zero is log Fano if and only if its modulo p reduction is globally F-regular for sufficiently large p. We proved that the conjecture holds true when X is a Mori dream space or a surface. Under the same assumption, that is, when X is a Mori dream space or a surface, we also proved that if its modulo p reduction is globally F-split for infinitely many p, then X is log Calabi-Yau.

该研究项目的目的是对Schwede-Smith的猜想做出肯定的答案，该猜想说，当且仅当其模量降低是全球fr-fraincuntion时，特征零的代数闭合字段的投射品种X对于足够大的P。我们证明，当X是Mori梦想空间或表面时，猜想是正确的。在相同的假设下，即当X是Mori Dream空间或表面时，我们还证明，如果其模量降低是无限多P的全球f-Split，则X是log calabi-yau。