Boundedness problems on the minimal model program and singularities

2015 Fiscal Year Final Research Report

• Project/Area Number: 24684003
• Research Category: Grant-in-Aid for Young Scientists (A)
• Allocation Type: Partial Multi-year Fund
• Research Field: Algebra
• Research Institution: Kyoto University
• Principal Investigator: KAWAKITA Masayuki 京都大学, 数理解析研究所, 准教授 (10378961)
• Project Period (FY): 2012-04-01 – 2016-03-31
• Keywords: 極小対数的食違い係数 / 昇鎖律 / 生成極限 / イデアル進半連続性 / 連結性補題 / 標準特異点 / 対数的標準特異点

Outline of Final Research Achievements

I studied the ACC for minimal log discrepancies, using generic limits introduced by de Fernex, Mustata and Kollar. I proved the discreteness of log discrepancies over all log canonical pairs for a fixed variety and fixed exponents, and obtained the ACC for minimal log discrepancies on local complete intersection singularities. Even when the exponents are not fixed, I proved the ACC for minimal log discrepancies greater than 1 on smooth 3-folds. Also, I showed the ideal-adic semi-continuity of minimal log discrepancies on surfaces.
As a boundedness problem of singularities, I proved that the index of a 3-fold strictly canonical singularity is at most 6.

Free Research Field

代数幾何学