Math 591 Algebraic Geometry

2006 Fall

Ali Sinan Sertöz
Faculty of Science, Department of Mathematics, Room: SA-121
Office Hours: Wednesday 13:40-15:30 or by appointment

MON 15:40-17:30 SAZ-02
WED    9:40-10:30 SAZ-21

This is an introductory lecture to algebraic geometry. We will assume nothing beyond a reasonable undergraduate education. Formally I intend to proceed along the lines of the book "An Invitation to Algebraic Geometry" but depending on the enthusiasm and the motivation of the class I may cover some cohomology, Riemann-Roch theorems and some classification theorems of curves and even of surfaces. Mentioning of the classification of threefolds need not be excluded either! For every extra subject I will provide class notes.

Recommended Text Books: 

Intended Subjects to be Covered
(This may change with class feedback.)

WEEK-1 Affine varieties
WEEK-2 Commutative algebra
WEEK-3 Projective varieties
WEEK-4 Quasi-projective varieties
WEEK-5 Classical constructions
WEEK-6 More classical constructions
WEEK-7 Smoothness
WEEK-8 Singularities
WEEK-9 Resolution of singularities
WEEK-10 Introduction to curves
WEEK-11 Classification of curves
WEEK-12 Introduction to surfaces
WEEK-13 Line bundles and vector bundles
WEEK-14 Sheaves
WEEK-15 Sheaf cohomology and examples


Grading and Exams: 

Homeworks 30%         
Take-Home Midterm 30%         
Take-Home Final 40%        

All homeworks and solutions will be announced here in Acrobat format (pdf) for which you need to download Acrobat Reader if that is not already installed on your machine.

Notes and Homework:
Affine Varieties


Take-Home Final Exam