Deformation theory of rings, schemes and sheaves. Construction/properties of Hilbert schemes. Representable functors, coarse and fine moduli spaces. Construction/properties of moduli spaces of sheaves and curves.
Learning outcome
After completing this course, the student should have fundamental knowledge of deformation theory and moduli theory in algebraic geometry.
Five hours of lectures and exercise sessions each week. In case of few students, the course may be organized as a guided self-study course.
Open for
PhD-studies in mathematics and physics
Course assessment
The faculty decides whether early dialogue will be held in all courses or in selected groups of courses. The aim is to collect student feedback for improvements during the semester. In addition, a digital course evaluation must be conducted at least every three years to gather students’ experiences.