MU25010 Chapters in Algebraic Geometry

Mathematical Institute in Opava
Winter 2018
Extent and Intensity
2/2/0. 6 credit(s). Type of Completion: zk (examination).
Guaranteed by
doc. RNDr. Hynek Baran, Ph.D.
Mathematical Institute in Opava
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
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
The course can also be completed outside the examination period.
The course is also listed under the following terms Winter 2012, Winter 2013, Winter 2014, Winter 2015, Winter 2016, Winter 2017, Winter 2019.
  • Enrolment Statistics (Winter 2018, recent)
  • Permalink: https://is.slu.cz/course/sumu/winter2018/MU25010