MU:MU25010 Chapters in Algebraic Geometry - Course Information

MU25010 Chapters in Algebraic Geometry

Extent and Intensity

2/2/0. 6 credit(s). Type of Completion: zk (examination).

Teacher(s)

doc. RNDr. Hynek Baran, Ph.D. (lecturer)
doc. RNDr. Hynek Baran, Ph.D. (seminar tutor)

Guaranteed by

doc. RNDr. Hynek Baran, Ph.D.
Mathematical Institute in Opava

Prerequisites (in Czech)

TYP_STUDIA(N)

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

• Geometry and Global Analysis (programme MU, N1101)

Course objectives (in Czech)

Mnohé geometrické a technické systémy lze popsat jako množinu řešení systému algebraických rovnic. Při jejich studiu lze s výhodou uplatnit metody algebraické geometrie. Přednáška zahrnuje základy klasické algebraické geometrie s důrazem na výpočetní postupy a aplikace.

Syllabus

• 1. Systems of polynomial equations and their solution: affine varieties, polynomial ideals, Hilbert Nullstellensatz.
  2. Groebner bases: ordering of monomials, Buchberger's algorithm, applications, arithmetic in quotient ring with respect to an ideal.
  3. Radical ideals, correspondence between ideals and varieties, sums, products and intersections, irreducible varieties and prime ideals.
  4. Triangular systems of polynomials, regular chains, arithmetic in regular chains.
  5. Applications in elementary geometry and robotics.
  

Literature

recommended literature
• D. A. Cox, J. B. Little, D. O'Shea. Ideals, Varieties, and Algorithms. Springer, 2007. info
• M. Kreuzer, L. Robbiano. Computational Commutative Algebra. Springer, 2000. info
• J. Bureš, J. Vanžura. Algebraická geometrie. SNTL, Praha, 1989. info

Language of instruction

Czech

Further Comments

Study Materials
The course can also be completed outside the examination period.

• Enrolment Statistics (recent)
  
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