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 by Caucher Birkar
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.

Familiarity with the basic concepts of the geometry of algebraic
varieties of dimension 1 and 2 would be useful but will not be assumed.

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.

To help me better understand the background of those interested in the course,
please complete the questionnaire at
this link
if you are considering attending this course.

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 9-10 in room MR5 at CMS.

First lecture will be on Thursday Jan 19.

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

This means that the lectures of Jan 24 and Jan 26
will be CANCELLED.

The second lecture will be on Teusday, Jan 31.

We will have two additional lectures to make up for my absence
on the following dates:

Monday Feb 6, 3-4pm, in MR11 and

Monday Feb 13, 3-4pm, in MR11.

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

Monday Feb 20 3-4pm, in MR11

Monday Mar 6 3-4pm, in MR11

Thursday Mar 16 9-10am MR5

REVISION CLASS:
The final revision class will be held on
Monday May 1
10am-1pm, in MR15.

All material will be posted on this website,
in the Example sheets section.

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

The deadline for turning in solutions is Saturday at noon for Monday classes and
Tuesday at noon for Thursday classes.

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

FINAL PAPER: By clicking here, you can see the text of the final paper for the course.

OFFICE HOURS:
If you have questions, doubts, problems with the class
I will be offering office hours on Mondays,
in the afternoon:

3-4pm on Mondays when we don't meet
for lectures or example classes, and right after the lectures/
example classes on those Mondays when we meet.

If you can't do it at those times, you can send me an email.