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Course, academic year 2023/2024
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Algebraic Geometry - NMAG401
Title: Algebraická geometrie
Guaranteed by: Department of Algebra (32-KA)
Faculty: Faculty of Mathematics and Physics
Actual: from 2020
Semester: winter
E-Credits: 5
Hours per week, examination: winter s.:2/2, C+Ex [HT]
Capacity: unlimited
Min. number of students: unlimited
4EU+: no
Virtual mobility / capacity: no
State of the course: taught
Language: English, Czech
Teaching methods: full-time
Teaching methods: full-time
Guarantor: Liran Shaul, Ph.D.
Class: M Mgr. MMIB
M Mgr. MMIB > Povinně volitelné
M Mgr. MSTR
M Mgr. MSTR > Povinné
Classification: Mathematics > Algebra
Annotation -
The course serves as an introduction to basic aspects of algebraic geometry. The discussed material includes the Zariski spectrum of a commutative ring and its relation to algebraic varieties, geometric aspects of localization of rings, maps between varieties, certain properties of abstract and projective varieties, and local properties of varieties (especially the Krull dimension and its properties).
Last update: Žemlička Jan, doc. Mgr. et Mgr., Ph.D. (12.09.2013)
Course completion requirements

In order to complete the course, the students must submit all homework, and to pass the final exam.

Last update: Shaul Liran, Ph.D. (25.09.2020)
Literature -

[1] I. R. Shafarevich: Basic Algebraic Geometry I, Second edition, Springer-Verlag, Berlin, 1994.

[2] A. Gathmann, Algebraic Geometry, http://www.mathematik.uni-kl.de/~gathmann/alggeom.php

[3] D. Cox, J. Little, D. O'Shea, Ideals, Varieties, and Algorithms, Springer-Verlag, New York, 1997.

[4] E. Kunz, Introduction to Commutative Algebra and Algebraic Geometry, Birkhäuser Boston, Inc., Boston, MA, 1985.

[5] M. F. Atiyah, I. G. MacDonald, Introduction to Commutative Algebra, Addison-Wesley Publishing Co., 1969.

[6] H. Matsumura, Commutative Ring Theory, Second edition, Cambridge University Press, 1989.

Last update: Šťovíček Jan, doc. RNDr., Ph.D. (12.09.2013)
Requirements to the exam

The course is completed with a written exam. The requirements for the exam correspond to the syllabus and will be applied to the extent to which the topic was presented in lectures. It will be also demanded that the student is able to work with particular examples and do computations to the extent exercised at problem sessions or in given homework.

Last update: Shaul Liran, Ph.D. (25.09.2020)
Syllabus -

1. the spectrum of a commutative ring and its relation to algebraic varieties,

2. geometric aspects of localization of rings,

3. maps between varieties,

4. abstract varieties,

5. projective varieties and their properties,

6. Krull dimension.

Last update: Šťovíček Jan, doc. RNDr., Ph.D. (12.09.2013)
Entry requirements -

Basics of commutative algebra on level of the course Introduction to commutative algebra.

Last update: Žemlička Jan, doc. Mgr. et Mgr., Ph.D. (28.06.2022)
 
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