MA9M6 Topics in Algebraic Geometry

The initial course description is here.

Lecture timetable

Mon 13:00 B3.03 from Mon 9th Jan 2023
Thu 13:00 in D1.07 except Week 5 Thu 9th Feb in B1.01	  	  	  	
Fri 11:00 B3.02

The lectures are broadcast on my Zoom account
    Meeting ID: 857 140 6186
    Password: 3MfD6v

Plan of lectures and partial lecture notes

The material is organised (if that is the right word) as a
series of Topics, each thought of as around one
week's worth of lectures. Informal lecture notes are
available for some of the material.

Week 1 What is a variety?

What is a quotient V/G of a variety by a group action? The main references for V/G are
Mumford, Abelian varieties, Chap. 2, Section 7, pp. 65-6
and my two Chapters Cyclic and Du Val   Week 1

Week 2

What is a scheme? How to define the structure sheaf of Spec R?
Proj R as the GGm quotient of Spec R \ V(m). The quasismooth
condition and cyclic orbifold points. The main references
are Hartshorne Chapter 2, Prop 2.2 for OX, and for Proj, my notes
on Graded rings and Hartshorne, Chapter 2, Section 7.   Week 2

Week 3 Cartier divisors and intersectdion numbers

My main reference for Cartier divisors is Mumford's book
Lectures on Curves on a Surface, Chap. 9. Intersection numbers
of curves on a surface are treated in Chap A of my Park City
book. Week 3