My Notes

Moduli Problems and GIT

I will study the basics of Geometric Invariant theory and then move on to explore VGIT by Dolgachev, Hu, Thaddeus, et al. 

Quotients 

Scheme theoretic viewpoint 

Interlude: Ample line bundle

Linearizations

Linearizations (continued)

Examples

What is a flip?

Hilbert-Mumford criterion

Finiteness of GIT quotients

Introduction to VGIT

Birational Geometry

Mori Dream Spaces

The goal is to follow the paper 'MDS and GIT' by Dolgachev and Hu.

1) Basics of Convex geometry

3) Mori Dream Spaces

Minimal Model Program

I) Overview
II) Sing 1
III) Sing 2
IV) Sing 3
V) Sing 4
VI) Sing 5
VII) Sing 6
VIII) MMP 1
X) MMP 3
The rest is in the 'New Outlook' section

New outlook of MMP

Recent techniques of MMP developed in here and here by Vladimir Lazić and Paolo Cascini.

Vector bundles on Curves

Moduli problems

Moduli II

Basics

Semi-stability

Hilbert Scheme

Moduli of Sheaves

Semistability

Families

Change of Polarization

Line bundles on Moduli Spaces

Bridgeland Stability

My notes so far.