[UAG] M. Reid, Undergraduate algebraic geometry, CUP. For other

books see below
#### Timetable for 2013-14:

Mon 11-12, MS.03

Tue 10-11, B1.01

Wed 10:00 B3.02 (normally an examples class with TA)

Fri 12-1, B1.01

The teaching assistant is Tom Ducat <Tom.Ducat@warwick.ac.uk>.

I will be away Fri 18th Oct and some days in Weeks 4, and I will

assign some alternative work.

The pdf and source TeX file of the book is available online

(unlinked, and currently without the graphics). If you need

the link, please let me know. I hope that one or two of the

students can help putting the graphics back into the TeX file.

### Assignment sheets:

There will be approximately 6 compulsory assignments counting for 30\%

of the credit.

Assignment 1, deadline TBA

first draft of Assignment 2, deadline TBA

### Prerequisites and suitability for 3rd year MMathers

The course uses basic definitions from most 1st and 2nd year courses,
including algebra, geometry, analysis. More than technical
prerequisites, the main requirement is the sophistication to work
simultaneously with ideas from several areas of mathematics: projective
geometry, rings and fields, basic topology and analysis. I would expect
the course to be harder than most for third year students, but not
impossible for those who are well motivated and can rise to a challenge.
The reward consists of access to 4th year and MSc/PhD courses and
projects in algebraic geometry.
Not on this year. I will eventually put up some information about
the graduate course MA610 (not for credit).
The PYDC entry is
here.
This is a first introduction to algebraic geometry at the MSc level. One
of the central topics is the relation between the commutative algebra of
graded rings and the geometry of projective varieties and singularities.
The emphasis is on concrete examples of curves, surfaces, projective
arieties and singularities, as illustrated in my Park City lecture notes
[Chapters] and in the book in progress [More Chapters]. Technical
foundational material, for example on commutative algebra and affine
schemes, on sheaves and coherent cohomology, will be introduced as
required, without detailed proofs. Students may wish to study more
material in a parallel self-help seminar (I can try to arrange exam
credit for this as necessary).

### Prerequisites

This is a second course in Algebraic Geometry, and it assumes
background knowledge at the level of the undergraduate course MA4A5 Algebraic Geometry or the material of [UAG] or
the first two chapters of Shafarevich, Basic algebraic geometry.
#### Timetable for 2006-07, Term 2:

Tue 2-3, B3.01

Thu 10-11, B3.01

Fri 11-12, B3.01
Several beginning postgraduates and visiting students will be
studying the subject at some level, and should take keep a look-out for
seminars at Warwick and elsewhere. (e.g. the COW and Calf that meets in
Warwick, Oxford, London, Bath, etc. Google "COW seminar").

### Books:

M. Reid, Undergraduate commutative algebra, CUP

M. Reid, Chapters on algebraic surfaces, in Complex algebraic
geometry (Park City, 1993), Amer. Math. Soc., Providence, RI, 1997,
3--159. The preprint version is available from my website + Surfaces

M. Reid, More chapters (book in preparation), see my website +
Surfaces

J.-P. Serre, Faisceaux algébriques cohérents, Ann. of Math.
61 (1955)

A. Borel and J.-P. Serre, Le théorème de Riemann-Roch, Bull.
Soc. Math. France 86 (1958) 97--136

I.R. Shafarevich, Basic algebraic geometry I, Springer, 1994

R. Hartshorne, Algebraic geometry, Springer Graduate Texts, 1977

H. Matsumura, Commutative ring theory, CUP
#### Assessment:

Three-hour written examination
#### Other material at the beginning graduate level

See the first
chapters of Chapters on algebraic surfaces, Park City 1993
index
and from More chapters (book in preparation):
Cyclic
surface quotient singularities

Graded
rings

See the
Homework.

See also my Surface
links

My front page
Google