CANKIRI KARATEKIN UNIVERSITY Bologna Information System


  • Course Information
  • Course Title Code Semester Laboratory+Practice (Hour) Pool Type ECTS
    Algebraic Curves MAT532 FALL-SPRING 3+0 E 6
    Learning Outcomes
    1-To comprehend the definitions of affine, projective spaces and algebraic curve
    2-To comprehend the basics of algebra-geometry relationship
    3-To find the transformations between algebraic curves
    4-To comprehend Riemann-Roch theorem and to do some of its applications
    5-To classify algebraic curves
    Prerequisites -
    Language of Instruction Turkish
    Responsible Assist. Prof. Dr. Nihal BİRCAN
    Instructors -
    Assistants The related lecturers of the department
    Resources 1) Algebraic Curves, William Fulton, Addison-Wesley, 1989. 2) Dodson, C.T.J., Poston, T. 2009. Tensor Geometry: The Geometric Viewpoint and its Uses, 2nd Edition. Springer, 434 p., Germany.
    Supplementary Book 1. Introduction to Algebraic Curves, Philip A. Griffiths, American Mathematical Society, 1989. 2. Plane Algebraic Curves, Gerd Fischer, American Mathematical Society, 2001. 3. Introduction to Plane Algebraic Curves, Ernst Kunz, Birkhauser, Bostan, 2005.
    Goals The aim of the course is to make an introduction to algebraic geometry, to study local and global properties of algebraic curves in affine and projective spaces, and to classify algebraic curves.
    Content Affine algebraic sets, the Hilbert basis theorem; Ideal-algebraic set correspondance, irreducibility; Affine varieties, coordinate rings; Polynomial maps, rational functions; Local rings, multiplicities; Tangent lines, intersection numbers; Projective spaces, projective sets; Projective varieties, multiprojective spaces; Curves in projective plane; Linear systems of curves, Bezout`s theorem; Zariski topology, algebraic function fields, dimension; Resolution of singularities, blowing up, nonsingular models; Divisors, diferantial, canonical divisors; Riemann-Roch theorem and its applications.
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