Welcome to Math 571! This course serves as an introduction to K3 surfaces and moduli spaces of sheaves on K3 surfaces. K3 surfaces play a special role in algebraic geometry. They play a central role in curve theory, in examples of holomorphic symplectic manifolds. Moduli spaces of sheaves on K3 surfaces provide the simplest examples of moduli spaces of sheaves on higher dimensional varieties. Via the Torelli Theorem, K3 surfaces are essentially linear algebraic objects, which makes their study accessible. The purpose of this course is to introduce you to many ideas and techniques in algebraic geometry using K3 surfaces as the main example. After developing the basic theory of K3 surfaces, we will give applications to linear systems on curves. We will discuss the Torelli Theorem and study the cone conjecture for K3 surfaces. We will then study moduli spaces of sheaves on K3 surfaces and introduce Bridgeland stability conditions and discuss some recent progress.
Lecturer: Izzet Coskun, coskun@math.uic.edu
Office hours: MWF 10:30-11, 12:00-12:30 and by appointment on Zoom
Venue: This course will be entirely online and will be conducted mainly on Zoom and Blackboard
Time: MWF 2:00-2:50 pm.
Main Text Huybrechts, Lectures on K3 surfaces.
Other recommended texts Huybrechts and Lehn, Moduli Spaces of Sheaves on Surfaces Beauville, Complex Algebraic Surfaces Barth, Hulek, Peters, Van de Ven, Compact Complex Surfaces
Grading The grade will be entirely based on homework exercises. I will regularly assign and discuss comcrete examples as homework.
Syllabus: Syllabus