This is a 16 lecture examinable course,
offered to Part III students. This is an advanced class
in Algebraic Geometry (AG).

I am assuming basic knowledge of varieties and schemes to a level equivalent
to the content of the course taught P.M.H. Wilson
in Michaelmas Term.

You may want to take this course if you want to
have a first glimpse of some more advanced topics in
Algebraic Geometry.

If all you have learnt so far in AG is
classical varieties and schemes, à la Hartshorne, you
may be wondering what people do with this kind of tools.

I would like to give an introduction to
some -- in some sense classical -- tools and ideas that
naturally arise from the basics of algebraic geometry.

In particular, I will try to explain how they can be used
towards understanding the structure of varieties.

PREREQUISITES:
The minimum requirement for those students wishing
to enroll in this class is their knowledge of basic concepts
from the Algebraic Geometry Part III course.

This roughly corresponds to Chapters 2 and 3 of Hartshorne's Algebraic Geometry.

In addition, in proving some of the theorems that will
be illustrated in the course we will make use of the notion
of scheme. Hence, it would be useful if you reviewed such
notion.

Familiarity with the basic concepts of the geometry of algebraic
varieties of dimension 1 and 2 would be useful.

For example, these topics are covered in the preliminary sections of
Chapters 4 and 5 of Hartshorne's Algebraic Geometry.

Students should have also some familiarity with concepts
covered in the Algebraic Topology Part 3 course
such as cohomology, duality and characteristic classes.

READINGS:
The following is a short list of books that may
be helpful in understanding the material covered
in the course.

If you want/need some guidance or
suggestions with the choice of books, please, get
in touch with the lecturer.

Some of these books may also be of interest to
those wanting to study even more algebraic geometry,
after attending this course.

W. Barth, C. Peters, A. Van de Ven,
*Compact Complex Surfaces.* Springer, 1984.

R. Hartshorne,
*Algebraic Geometry.* Springer, 1997.

J. Kollár, S. Mori,
*Birational geometry of algebraic varieties.*
Cambridge University Press, 1998.

R. Lazarsfeld,
*Positivity in Algebraic Geometry, Vol. 1.*
Springer, 2004.

D. Mumford,
*Lectures on Curves on an Algebraic Surface.*
Princeton University Press, 1966.

LECTURER:
Roberto Svaldi.
To contact me, use the email.

My office, C2.01, is located in Pavillion C at CMS.

LECTURES
are held Tuesday and Thursdays 10-11 in room MR13 at CMS.

First lecture will be on Thursday Jan 18.

Attention:
I will be away on Week 1
of the term.

This means that the lectures of Jan 23 and Jan 25
will be CANCELLED.

The second lecture will be on Tuesday, Jan 30.

We will have two additional lectures to make up for my absence
on February 10 and 17, at the same time and in the same classroom
as the other lectures.

ATTENTION: the class of February 17th will be held in MR14.

EXAMPLE CLASSES:
There will also be 3 example classes
with the following
schedule:

Tuesday Feb 27, 3-4.30pm, MR6

Tuesday Mar 13, 3-4.30pm, MR6

Thursday Apr 26, 10-11.30am, MR14

REVISION CLASS:
There will be a final revision class to be held
in May.

The schedule for that will appear here towards
the end of Lent Term.
All material will be posted on this website,
in the Example sheets section.

In each example sheet, there will be a few questions whose solutions
you can write up and turn in to me for marking.

Solutions can be delivered to my personal pigeonhole in the DPMMS mailboxes
at the entrance of CMS

OFFICE HOURS: If you have questions, doubts, problems with the class I will be offering office hours. You should get in contact with me, via email, to schedule a time.