Various problems related to the classification in higher dimensional birational geometry

2017 Fiscal Year Final Research Report

• Project/Area Number: 25287005
• Research Category: Grant-in-Aid for Scientific Research (B)
• Allocation Type: Partial Multi-year Fund
• Section: 一般
• Research Field: Algebra
• Research Institution: Kyoto University
• Principal Investigator: Mori Shigefumi 京都大学, 高等研究院, 特別教授 (00093328)
• Research Collaborator: Prokhorov Yuri ステクロフ研究所, 教授
• Project Period (FY): 2013-04-01 – 2018-03-31
• Keywords: Qコニック束 / 因子収縮射 / フリップ収縮射 / 反標準線形系 / Du Val特異点 / 端末特異点 / Qデルペゾ束 / 極小モデルプログラム

Outline of Final Research Achievements

We study extremal contraction morphisms f to S of a terminal threefold X such that the inverse image F of a point s is a curve, and try to classify the neighbourhood of F especially when F is irreducible. They consist of three kinds, flipping contractions, divisorial contractions, and Q-conic bundles. Among them, flipping contractions were classified, and the other two kinds are studied. There are at most two non-Gorenstein points on F, and the classification of the case of one non-Gorenstein point has been completed.

Free Research Field

数物系科学