M8140 Algebraic Geometry

Faculty of Science
Spring 2026
Extent and Intensity
2/2/0. 6 credit(s). Type of Completion: zk (examination).
In-person direct teaching
Teacher(s)
doc. Lukáš Vokřínek, PhD. (lecturer)
Guaranteed by
doc. Lukáš Vokřínek, PhD.
Department of Mathematics and Statistics – Departments – Faculty of Science
Supplier department: Department of Mathematics and Statistics – Departments – Faculty of Science
Timetable
Mon 16. 2. to Fri 22. 5. Mon 8:00–9:50 M4,01024
  • Timetable of Seminar Groups:
M8140/01: Mon 16. 2. to Fri 22. 5. Tue 10:00–11:50 MZAS,02015, L. Vokřínek
Prerequisites
Sound knowledge of algebra, linear algebra and geometry.
Course Enrolment Limitations
The course is also offered to the students of the fields other than those the course is directly associated with.
fields of study / plans the course is directly associated with
Abstract
The lecture gives an overview of the basics of the classical algebraic geometry, presented mainly from the geometric point of view.
Learning outcomes
Passing the course the students will
- be able to compute Grobner bases of ideals and solve relevant algebraic and geometric problems;
- understand the basics of the theory of affine and projective varieties;
- be able to solve simple problems concerned with affine and projective varieties;
- understand the basic constructions in the theory of schemes
Key topics
  • Closed subsets in affine spaces
  • Closed subsets in projective spaces
  • Local properties of algebraic varieties
  • Planar algebraic curves and varieties of codimension one
  • Introduction to the theory of schemes
Study resources and literature
  • HULEK, Klaus. Elementary algebraic geometry. Translated by Helena Verrill. Providence, Rhode Island: American Mathematical Society, 2003, viii, 213. ISBN 0-8218-2952-1. info
  • BUREŠ, Jarolím and Jiří VANŽURA. Algebraická geometrie. Vyd. 1. Praha: SNTL - Nakladatelství technické literatury, 1989, 327 s. info
Approaches, practices, and methods used in teaching
Lectures and tutorials.
Method of verifying learning outcomes and course completion requirements
Written and oral examination. Requirements: knowledge of the theory from the lectures, ability to solve problems at the level of the tutorials.
Language of instruction
Czech
Further comments (probably available only in Czech)
The course is taught once in two years.
Teacher's information
The lectures are usually in Czech or in English as needed, and the relevant terminology is always given with English equivalents. Assessment in all cases may be in Czech and English, at the student's choice.
The course is also listed under the following terms Spring 2008 - for the purpose of the accreditation, Spring 2000, Autumn 2000, Spring 2002, Spring 2004, Spring 2006, Spring 2008, Spring 2010, Spring 2012, spring 2012 - acreditation, Spring 2014, Spring 2016, spring 2018, Spring 2020, Spring 2022, Spring 2024.
  • Enrolment Statistics (recent)
  • Permalink: https://is.muni.cz/course/sci/spring2026/M8140