Positivity in Algebraic Geometry, Part III, L18

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.


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 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.

Course calendar


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, MR12


REVISION CLASS: There will be a final revision class to be held on May 15th, 10-13, in MR12.
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

Example sheets


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.