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Introduction to the Minimal Model Program and Singularities

Course Description
This course will introduce the Minimal Model Program (MMP), including singularities in MMP and the cone theorem. We will also study 3-dimensional terminal and canonical singularities in more details. Topics will include:
• Mori’s existence theorem of rational cuves
• Singularities in MMP
• Cone theorems
• Elliptic surface singularities and 3-fold canonical singularities
• Classification of 3-fold terminal singularities
• Existence of 3-fold flips (after Shokurov)

Course Objectives
The goal of this course is to provide general knowledge and skills in
birational geometry.

Prerequisites
Knowledge of algebraic geometry is required:
• R. Hartshornes, Algebraic Geometry
• A. Beauville, Complex algebraic surfaces
Preliminary knowledge of the theory of deformation will be very helpful.

Textbook
J. Kollar and S. Mori, Birational Geometry of Algebraic Varieties, 1998

Date: Every Monday and Thursday
Sep. 4 ~ Dec. 15, 2023
Time: 10 : 20 ~ 12 : 10
Place: Room 201 (Astro-Math Building 2F, NTU)
Speaker: Sz-Sheng Wang (Academia Sinica)

Available Talk List

2023-09-04 (Mon.)	Motivation of the Mori program
2023-09-07 (Thu.)	Cone of divisors
2023-09-11 (Mon.)	Existence of rational curves I
2023-09-14 (Thu.)	Existence of rational curves II
2023-09-18 (Mon.)	Vanishing theorem I
2023-09-21 (Thu.)	Vanishing theorem II
2023-09-25 (Mon.)	Singularities in the MMP I
2023-09-28 (Thu.)	Singularities in the MMP II
2023-10-02 (Mon.)	Cone theorem I
2023-10-05 (Thu.)	Cone theorem II
2023-10-12 (Thu.)	Cone theorem III
2023-10-16 (Mon.)	Surface singularities I
2023-10-19 (Thu.)	Surface singularities II
2023-10-23 (Mon.)	Surface singularities III
2023-10-26 (Thu.)	Surface singularities IV
2023-10-30 (Mon.)	Canonical and terminal 3-fold singularities I
2023-11-02 (Thu.)	Canonical and terminal 3-fold singularities II
2023-11-06 (Mon.)	Canonical and terminal 3-fold singularities III
2023-10-09 (Thu.)	Canonical and terminal 3-fold singularities IV
2023-11-13 (Mon.)	Classification of terminal 3-fold singularities I
2023-11-16 (Thu.)	Classification of terminal 3-fold singularities II
2023-11-20 (Mon.)	Classification of terminal 3-fold singularities III
2023-11-23 (Thu.)	Classification of terminal 3-fold singularities IV
2023-11-27 (Mon.)	Flips and Flops I
2023-11-30 (Thu.)	Flips and Flops II