Singularities on algebraic varieties

2014 Fiscal Year Final Research Report

• Project/Area Number: 22340004
• Research Category: Grant-in-Aid for Scientific Research (B)
• Allocation Type: Single-year Grants
• Section: 一般
• Research Field: Algebra
• Research Institution: The University of Tokyo
• Principal Investigator: ISHII Shihoko 東京大学, 数理(科)学研究科(研究院), 教授 (60202933)
• Co-Investigator(Kenkyū-buntansha): WATANABE Keiichi 日本大学, 文理学部, 教授 (10087083) ; TAKAGI Shunsuke 東京大学, 大学院数理科学研究科, 准教授 (40380670) ; TOMARU Tadashi 群馬大学, 医学部, 教授 (70132579)
• Project Period (FY): 2010-04-01 – 2015-03-31
• Keywords: 特異点 / 弧空間 / 極小対数的食い違い数

Outline of Final Research Achievements

We proved the Inversion of Adjunction formula according to the minimal log discrepancies which is defined by Mather-Jacobian discrepancies. By means of this discrepancies we introduced MJ-canonical singularities and also MJ-multiplier ideal. We also prove that the ideal has good properties; vanishing theorem, subaddidivity property and so on. In general MJ-minimal log discrepancy is greater than of equal to the dimension of the variety, we determined all MJ , we determined singularities whose MJ-minimal log discrepancy.

Free Research Field

代数幾何学