Yuri Prokhorov - Effective Results in the Three-Dimensional Minimal Model Program

Explore recent developments in the three-dimensional minimal model program in this 42-minute lecture by Yuri Prokhorov. Gain insights into the basic operations, steps, and outcomes of the MMP. Delve into terminal 3-fold singularities, general elephant theorems, and the classification of extremal curve germs. Examine divisorial contractions, Q-del Pezzo fibrations, and the effective boundedness of Q-Fano 3-folds. Access accompanying slides for visual support and deeper understanding of this advanced mathematical topic.

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