Kaisa_2012_3_photo by Veikko Somerpuro

Algebraic geometry studies the geometric properties of the set of solutions of systems of polynomial equations. After the course, the student will be familiar with the fundamental concepts of algebraic varieties, which are the geometric manifestations of these solutions. The main goals are (1) working knowledge of basic elements of affine and projective geometry (2) familiarity with explicit examples, which are fundamental for the whole theory, including plane curves, Grassmannian, Veronese and Segre varieties, etc.

Ilmoittaudu
10.2.2020 klo 09:00 - 9.3.2020 klo 23:59

Aikataulu

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PäivämääräAikaOpetuspaikka
Ma 9.3.2020
10:15 - 12:00
Ke 11.3.2020
12:15 - 14:00
Pe 13.3.2020
10:15 - 12:00
Ma 16.3.2020
10:15 - 12:00
Ke 18.3.2020
12:15 - 14:00
Pe 20.3.2020
10:15 - 12:00
Ma 23.3.2020
10:15 - 12:00
Ke 25.3.2020
12:15 - 14:00
Pe 27.3.2020
10:15 - 12:00
Ma 30.3.2020
10:15 - 12:00
Ke 1.4.2020
12:15 - 14:00
Pe 3.4.2020
10:15 - 12:00
Ma 6.4.2020
10:15 - 12:00
Ke 8.4.2020
12:15 - 14:00
Pe 17.4.2020
10:15 - 12:00
Ma 20.4.2020
10:15 - 12:00
Ke 22.4.2020
12:15 - 14:00
Pe 24.4.2020
10:15 - 12:00
Ma 27.4.2020
10:15 - 12:00
Ke 29.4.2020
12:15 - 14:00

Kuvaus

Master's Programme in Mathematics and Statistics
Algebra II
Topology and Differential Geometry can be useful, since most of the concepts in the course are algebraic versions of concepts coming from topology and differential geometry. However, the course aims at self-consistence in presenting the topics.
As the name suggests, algebraic geometry studies the geometric properties of the set of solutions of systems of polynomial equations. After the course, the student will be familiar with the fundamental concepts of algebraic varieties, which are the geometric manifestations of these solutions. The main goals are (1) working knowledge of basic elements of affine and projective geometry (2) familiarity with explicit examples, which are fundamental for the whole theory, including plane curves, Grassmannian, Veronese and Segre varieties, etc.
"Content List (time permitting) - Zariski Topology - Algebraic Sets - Hilbert's Nullstellensatz - Regular and Rational maps - Affine Varieties - Zariski Tangent Space - Derivations - Smooth points - (Quasi)Projective Varieties - Segre and Veronese varieties - Grassmannians - Plane curves"
Lecture Notes and other textbooks recommended during the course
Weekly reading group meetings for discussing the course material and exercises.
The grade is determined by a combination of exercise points, and a grade from the exam or presentation