Winter 2021

Winter 2021: This semester I am teaching an Advanced Graduate Course intended for 3rd year or above graduate students, postdocs and interested faculty members. It will be an online course taught over Zoom. Meeting ID and Passwords will sent every week via emails. An outline of the course is given below.

Title: Fundamental Theorems of the Minimal Model Program.

Lecture Schedule: Monday and Wednesday, 11:30 AM-1:00 PM. The first lecture will be held on February 1st (Monday).

Main Texts: 1. ``Birational Geometry of Algebraic Varieties'' by Kollár and Mori.

2. ``Introduction to the Minimal Model Program'' by Kawamata, Matsuda, and Matsuki.

3. ``Classification of Higher Dimensional Algebraic Varieties'' by Hacon and Kovács.

Course Content: We will do a rigorous study of Chapter 3 materials of the Kollar Mori book. It includes the following topics: Non-Vanishing Theorem, Base-Point Free Theorem, Rationality Theorem, and Cone Theorem. We will also prove the necessary and sufficient conditions for the existence of Flips, reduction to Pl-flips, special termination, and other properties of flips. We will also talk about the Abundance Conjecture and its proof in dimension 3.

Prerequisites: The previous course on the ``Singularities of the Minimal Model Program''. The lecture videos and notes can be found here: Singularities of MMP.

Additional References: Following texts may be used for additional references.

1. Flips for 3-folds and 4-folds by A. Corti.

2. Lecture Notes on MMP by Hacon.

Lecture Notes (PDF): Lecture 1, Lecture 2, Lecture 3, Lecture 4, Lecture 5, Lecture 7, Lecture 8, Lecture 9, Lecture 10, Lecture 11, Lecture 12, Lecture 13, Lecture 14, Lecture 15, Lecture 16, Lecture 17, Lecture 18, Lecture 19, Lecture 20, Lecture 21, Lecture 22, Lecture 23, Lecture 24, Lecture 25, Lecture 26,

Lecture Videos (YouTube Link): Lecture 1, Lecture 2, Lecture 3, Lecture 4, Lecture 5, Lecture 6, Lecture 7, Lecture 8, Lecture 9, Lecture 10, Lecture 11, Lecture 12, Lecture 13, Lecture 14, Lecture 15, Lecture 16, Lecture 17, Lecture 18, Lecture 19, Lecture 20, Lecture 21, Lecture 22, Lecture 23, Lecture 24, Lecture 25, Lecture 26,