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Introduction to Algebraic Geometry - NGEM001

Title:	Úvod do algebraické geometrie
Guaranteed by:	Mathematical Institute of Charles University (32-MUUK)
Faculty:	Faculty of Mathematics and Physics
Actual:	from 2011
Semester:	summer
E-Credits:	3
Hours per week, examination:	summer s.:2/0, Ex [HT]
Capacity:	unlimited
Min. number of students:	unlimited
4EU+:	no
Virtual mobility / capacity:	no
State of the course:	cancelled
Language:	Czech
Teaching methods:	full-time
Teaching methods:	full-time

Guarantor:	doc. RNDr. Petr Somberg, Ph.D. prof. RNDr. Pavel Pudlák, DrSc.
Class:	Riemannova geometrie
Classification:	Mathematics > Geometry

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Annotation -

Last update: T_MUUK (23.05.2003)

Projective algebraic varieties, their basic geometric properties and algebraic and geometric invariants.

Literature - Czech

Last update: RNDr. Pavel Zakouřil, Ph.D. (05.08.2002)

1. J.Harris : Algebraic Geometry. A First course, Springer GTM 133

2. J.Bureš, J.Vanžura \" Algebraická geometrie, SNTL 1989

Syllabus -

Last update: T_MUUK (23.05.2003)

1. Projective space and its properties. 2. Affine and projective varieties. Ideals vs varieties. 3. Regular functions and regular maps. Veronese and Segre mappings. 4. Grassman varieties and their subvarieties. 5. Rational functions and rational maps. 6. Birational correspondence. 7. Curves and their embedding. 8. Divisors and line bundles on curves, Riemann-Roch Theorem and its consequences. 9. Dimension and degree of variety, Hilbert polynomial.