Linear Systems, Part III, L17

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.


Practical Info

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.

Course calendar

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

Example sheets

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.