Welcome to MATH 571! This course will introduce basic techniques that should be familiar to every working algebraic geometer. We will start with a unit in intersection theory, covering Chern classes and basic enumerative problems. We will then discuss curves and surfaces and birational geometry. We will conclude with a unit on Bridgeland stability and the geometry of the Hilbert scheme of points on surfaces.

** Prerequisites: ** MATH 552 and MATH 553, or a year of algebraic geometry at the level of Hartshorne or Griffths and Harris

** Time and Venue: ** MWF 10:00--10:50 in AH 302 (NOTE TIME AND VENUE CHANGE).

** Lecturer: ** Izzet Coskun

** Office: ** SEO 423

** Required text: ** There are no required textbooks. I will list references for each unit.

** Grading: ** There will be problem sets. These problem sets will account for your entire grade. You must turn in a 100 problem solutions by in order to receive an A in the course.

** Homework: ** Here are the suggested problems from Eisenbud and Harris:

Week I: 1.42, 1.43, 1.44, 1.46, 1.48, 1.50, 1.51, 1.53, 1.54, 1.59, 1.64, 1.65, 1.66

Week II: 1.67, 1.68, 1.69, 1.70, 1.71, 1.72, 1.73, 1.74, 1.75, 1.76, 1.77, 2.10, 2.11, 2.12, 2.13, 2.14,

Week III: 2.19, 2.21, 2.22, 2.24, 2.25, 2.27, 2.28, 2.29, 2.33, 2.37, 2.38, 2.39, 2.40, 2.41, 2.42, 2.43, 2.44, 3.15, 3.16, 3.19, 3.20, 3.21

Week IV: 3.24, 3.25, 3.29, 3.31, 3.32, 3.33, 3.34, 3.36, 3.37, 3.38

Week V: 7.20, 7.21, 7.22, 7.23, 7.24, 7.25, 7.27, 7.28. 8.47, 8.48, 8.49. 8.50, 8.51

Week VI: 8.52, 8.53, 8.55, 8.56, 8.57, 8.63, 8.64, 8.65, 8.67, 8.68, 8.78-8.80

Week VII: 9.21-9.25, 9.26, 9.28, 9.29, 9.30, 9.36, 9.39, 9.42, 9.44-9.47