This course covers recent developments in the three-dimensional minimal model program, including an overview, basic operations, steps, outcomes, terminal 3-fold singularities, extremal curve germs, divisorial contractions, and effective boundedness of Q-Fano 3-folds. The course aims to teach the skills needed to understand and work with these concepts. The teaching method involves a brief review and explanation of the key topics. This course is intended for individuals interested in advanced topics in algebraic geometry and the minimal model program.
Yuri Prokhorov - Effective Results in the Three-Dimensional Minimal Model Program
International Mathematical Union via YouTube
Overview
Syllabus
Intro
Minimal model program (MMP): Overview
Basic operations in the MMP
Steps of the MMP
Outcome of the MMP
Terminal 3-fold singularities
Example of a terminal 3-fold singularity
General elephant (local version)
Classification of extremal curve germs: general strategy
General elephant: irreducible central fiber
General elephant: consequences and generalizations
From general elephant to hyperplane sections
Example of semistable extremal curve germs
Classification of irreducible exceptional curve germs
Divisorial contractions to a point
Q-del Pezzo fibrations
Effective boundedness of Q-Fano 3-folds
Taught by
International Mathematical Union
