The initial course description is **
****
here. **

### Lecture timetable

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**