SubjectsSubjects(version: 806)
Course, academic year 2017/2018
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Algebraic Geometry - NMAG401
Czech title: Algebraická geometrie
Guaranteed by: Department of Algebra (32-KA)
Faculty: Faculty of Mathematics and Physics
Actual: from 2016
Semester: winter
E-Credits: 5
Hours per week, examination: winter s.:2/2 C+Ex [hours/week]
Capacity: unlimited
Min. number of students: unlimited
State of the course: taught
Language: English, Czech
Teaching methods: full-time
Guarantor: doc. RNDr. Jan Šťovíček, Ph.D.
Class: M Mgr. MSTR
M Mgr. MSTR > Povinné
Classification: Mathematics > Algebra
Annotation -
Last update: Mgr. et Mgr. Jan Žemlička, Ph.D. (12.09.2013)

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

[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.

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

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.

 
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