Please note! Course description is confirmed for two academic years, which means that in general, e.g. Learning outcomes, assessment methods and key content stays unchanged. However, via course syllabus, it is possible to specify or change the course execution in each realization of the course, such as how the contact sessions are organized, assessment methods weighted or materials used.


Credits: 5

Schedule: 27.02.2024 - 12.04.2024

Teacher in charge (valid for whole curriculum period):

Teacher in charge (applies in this implementation): Oscar Kivinen

Contact information for the course (applies in this implementation):

Lecturer: Prof. Oscar Kivinen (, office hours by appointment/whenever my door is open) 

TA: Lassi Virtanen (

CEFR level (valid for whole curriculum period):

Language of instruction and studies (applies in this implementation):

Teaching language: English. Languages of study attainment: English


  • applies in this implementation

    This course is aimed to give an introduction to algebraic geometry. In particular, in this course you will learn the basic definitions in the theory of varieties and schemes and see many examples of these. About a half of this course will be devoted to developing more algebraic notions, including a refresher on commutative algebra. This will be intermixed with another half of more geometric, low-dimensional ideas, in order to develop intuition for the notions encountered.

    Algebraic geometry is a vast field, the basics of which are "common knowledge" useful to any mathematician. The course will also include a small project on a topic of your choice (for example: algebraic groups, elliptic curves, algebraic surfaces, toric varieties, Grassmannians, or sheaf cohomology).

    At the end of this course, the student will be able to

    • use basic notions from algebraic geometry, like the Zariski topology and affine/projective varieties
    • recall various properties of varieties/schemes/morphisms, blowing up, (quasi-)coherent sheaves
    • prove basic theorems in the theory of algebraic curves
    • self-study more advanced topics in algebraic geometry

Assessment Methods and Criteria
  • applies in this implementation

    Teaching methods: lectures Tue 12-14, Thu 10-12 and exercises Fri 12-14.

    Assessment methods: weekly exercise sets (75%) and a final expository paper (25%) on a topic of your choice.

    • Exercises (75%). Roughly each week, I will post a problem set to be discussed during Friday's exercise session. The problems marked with an asterisk are to be returned the next week (the precise due date will be marked on the exercise sheet).
    • A final paper will be due at the end of the period. This will be a brief (roughly 5-10 page) expository paper on a supplemental topic of your choice. The paper is due at midnight on Thursday, April 11. Detailed instructions will be published on the MyCourses page.

  • applies in this implementation

    Contact hours 36h (no compulsory attendance), self-study ca 100h.


Study Material
  • applies in this implementation

    There is no single textbook we will follow, but references to relevant texts or notes will be given throughout the course.

    Much of the material will be from 

    • B. Osserman, "A Concise Introduction to Algebraic Varieties"
    • R. Hartshorne, "Algebraic Geometry", Chapters I-II
    • I. Shafarevich, "Basic Algebraic Geometry I"
    • R. Miranda, "Algebraic Curves and Riemann Surfaces"
    • Q. Liu, "Algebraic Geometry and Arithmetic Curves"

Substitutes for Courses