MAT 536  Algebra III: Introduction to Algebraic Geometry   Fall 2009 

TuTh 9:50am-11:10am Math 4-130

Instructor: Ljudmila Kamenova
Office: Math Tower 3-115
Office hours: TuTh 11:10am-12:10pm

The Instructor may be reached by e-mail at
Feel free to send me an e-mail or drop by outside of office hours.

Introduces the basic notions and techniques of modern algebraic geometry. Algebraic sets, Hilbert's Nullstellensatz and varieties over algebraically closed fields. We relate varieties over the complex numbers to complex analytic manifolds. For varieties of dimension one (i.e. curves) we discuss the genus, divisors, linear series, line bundles and Riemann-Roch's theorem.


1. Algebraic sets, Hilbert basis theorem, Nullstellensatz.

2. Affine varieties, varieties and morphisms.

3. Projective varieties, Veronese and Segre maps.

4. Complete varieties.

5. Noetherian topological spaces.

6. Rational functions, rational maps, separated varieties.

7. Non-singular varieties, Jacobians, manifolds.

8. Sheaves and schemes.

9. Divisors and line bundles.

10. Algebraic curves.

Recommended books:

Grading: The final course grade will be determined based entirely on homework.


HW 1 (due 9/10/09): Click here for the problems.

HW 2 (due 9/24/09): Click here for the problems.

HW 3 (due 10/1/09): Click here for the problems.

HW 4 (due 10/8/09): Click here for the problems.

HW 5 (due 10/15/09): Click here for the problems.

HW 6 (due 10/29/09): Click here for the problems.

HW 7 (due 11/5/09): Click here for the problems.

HW 8 (due 11/19/09): Click here for the problems.

HW 9 (due 12/8/09): Click here for the problems.

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