Last update: doc. 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).
Last update: doc. Mgr. et Mgr. Jan Žemlička, Ph.D. (12.09.2013)
Přednáška slouží jako úvod do základních aspektů algebraické geometrie. Probíraná látka zahrnuje Zariského spektrum komutativního okruhu a jeho vztah k algebraickým varietám, geometrický význam lokalizace okruhů, zobrazení mezi varietami, některé vlastnosti abstraktních a projektivních variet a lokální vlastnosti variet (především pojem Krullovy dimenze a jeho vlastnosti).
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.
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.
Last update: doc. RNDr. Jan Šťovíček, Ph.D. (12.09.2013)
1. spektrum komutativního okruhu a jeho vztah k algebraickým varietám,
