MATH 430/505 - Complex Geometry
Spring 2015

Ali Sinan Sertöz
Faculty of Science, Department of Mathematics, Room: SA-121

Office Hours:
Thursday 13:40-15:30

Text Books:
Complex Geometry, An Introduction, Daniel Huybrechts, Universitext, Springer-Verlag, 2005. (first three chapters)
Principles of Algebraic Geometry, Philip Griffiths and Joseph Harris, Wiley Interscience, 1978. (parts of chapter 0)
A Survey of the Hodge Conjecture, James D. Lewis, CRM Monograph Series Vol: 10, American Mathematical Society, 1991. (selected sections)
The Hodge Theory of Projective Manifolds, Mark Andrea de Cataldo, Imperial College Press, 2007. (to be read only after the course is over)

Using complex numbers in geometry opens up unexpected and surprising new avenues of exploration. We will weave the course around the famous Hodge conjecture so that at any moment we will have a solid motivation to embrace the new techniques and concepts that arise.

For an extended synopsis you may want to read this summary.

For a brief history of the Hodge conjecture you may read this.

And finally, here is a synopsis of Hodge theory by Emre Sertöz who took this course back in 2010:


Also the web page of the course in 2010 contains some more information.

TUE 13:40-15:30 SAZ-19  
THU 15:40-16:30 SAZ-19  

Exams and Grading:

 Midterm 1 25%  Take-Home  Due on 16 April 2015 Class time   Solution 
 Midterm 2 25%  Take-Home  Due on 12 may 2015, Class time   Solution 
 Final 35%  Take-Home  20 May 2015 Wednesday, 15:30   Solution  
 Homework 15%  Take-Home

Note: After each take-home work there may be in class quizzes to check your understanding of what you wrote in the take-home work. The questions will be tailored separately for each student. Your questions will be related to those answers you gave in the take-home work. Your grade for that take-home will be determined after this quiz. 

By Yönetmelik Madde 4.7  here is our FZ grade policy:
Failure to attend at least 50% of the classes or averaging less than 40% from the two midterms will result in an FZ grade. 


Homework-1  Due on 10 February 2015 class time  Solution
Homework-2  Due on 14 April 2015 Class time  Solution
Homework-3  Due on 21 April 2015 Class time  Solution
Homework-4  Due on 13 May 2015 Wednesday  Solution
Homework-5 Due on 14 May 2015 Thursday  Solution

The course will be graded according to  the following catalogue:

[40,44] D
[45,49] D+
[50,53] C-
[54,56] C
[57,59] C+
[60,62] B-
[63,65] B
[66,68] B+
[69,71] A-
[72,100] A



The topics below will be discussed only to the extend that they are required to understand the statement and immediate verifications of the Hodge conjecture. 



Subjects to be covered
1 3, 5 Feb Several complex variables
2 10, 12 Feb  Complex manifolds
3 17, 19 Feb Affine varieties
4 24, 26 Feb Projective varieties
5 3, 5 Mar Sheaf theory
6 10, 12 Mar Cech cohomology
7 19 Mar de Rham cohomology
8 24, 26 Mar Dolbeault cohomology
9 31 Mar, 2 Apr  Algebraic cycles
10 7, 9 Apr Poincare duality
11 14, 16 Apr Harmonic forms
12 21 Apr Hodge decomposition
13 28, 30 Apr Hodge conjecture - popular version
14 5, 7 May Hodge conjecture - general version
15 12, 14 May What is known about the Hodge conjecture


Old Exams are on Old Courses Web Page


Contact address is: