Kaisa_2012_3_photo by Veikko Somerpuro

Please check the Moodle page for the new organization of the course.

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

Viestit

Roberto Fringuelli

Julkaistu, 20.4.2020 klo 20:22

Notes of Week 6 added to Material
Homework 6 added to Task, deadline Monday 27, please submit using the link Homework Assignment 6 in the Moodle page

Roberto Fringuelli

Julkaistu, 30.3.2020 klo 21:48

Notes of Week 4 added to the Material.
Homework 4 added to the task, please submit using the link Homework Assignment 4 in the Moodle page

Roberto Fringuelli

Julkaistu, 26.3.2020 klo 7:52

In the previous version of Homework 3, the Exercise 2 was uncomplete. The new version is ok.

Roberto Fringuelli

Julkaistu, 23.3.2020 klo 22:25

New Homework 3 added to the task. Please submit using the link Homework Assignment 3 in the Moodle page

Roberto Fringuelli

Julkaistu, 23.3.2020 klo 10:46

Notes of the 3rd week added to the material. Homework 3 will be added tonight.

Roberto Fringuelli

Julkaistu, 20.3.2020 klo 11:30

Notes of the 2nd week added to the material

Aikataulu

Tästä osiosta löydät kurssin opetusaikataulun. Tarkista mahdolliset muut aikataulut kuvauksesta.

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

Materiaalit

Recommended literature:
J. Harris, Algebraic geometry (a first course), Graduate Texts in Math. No. 133. Springer-Verlag, New York-Heidelberg, 1977.
R. Hartshorne, Algebraic geometry, Graduate Texts in Math. No. 52. Springer-Verlag, New York-Heidelberg, 1977.
R. Miles. Undergraduate algebraic geometry. London Mathematical Society Student Texts, 12. Cambridge University Press, Cambridge, 1988.

Tehtävät

Final Homework

Homework 1

Homework 2

Homework 3

Homework 4

Homework 5

Homework 6

Solutions HW 1

Solutions HW 2

Solutions HW 3

Solutions HW 4

Solutions HW 5

Solutions HW 6

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