Algebraic Geometry

Course Information
TitleΑΛΓΕΒΡΙΚΗ ΓΕΩΜΕΤΡΙΑ / Algebraic Geometry
Cycle / Level2nd / Postgraduate
Teaching PeriodSpring
CoordinatorDimitrios Poulakis
Course ID40000025

Programme of Study: PMS Tmīmatos Mathīmatikṓn (2018-sīmera)

Registered students: 10
OrientationAttendance TypeSemesterYearECTS

Class Information
Academic Year2019 – 2020
Class PeriodSpring
Faculty Instructors
Weekly Hours3
Class ID
Type of the Course
  • Scientific Area
Course Category
Specific Foundation / Core
Mode of Delivery
  • Face to face
Digital Course Content
The course is also offered to exchange programme students.
Language of Instruction
  • Greek (Instruction, Examination)
General Competences
  • Adapt to new situations
  • Make decisions
  • Work autonomously
  • Work in teams
  • Work in an international context
  • Generate new research ideas
  • Be critical and self-critical
  • Advance free, creative and causative thinking
Course Content (Syllabus)
Affine Varieties: Algebraic Sets in Αn, Affine and quasi-affine Varieties, Hilbert's Nullstellensatz, Coordinate Rings, Noether's Spaces. Projective Varieties: Algebraic Sets in Pn, Projective Nullstellensatz, Projective Closure of an Affine Variety. Morphisms of Varieties: Regular Functions, Function Fields of One Variable, Basic properties of Morphisms, Finite Morphisms, Rational maps. Product of Varieties: Product of Affine Varieties, Product of Projective Varieties, Segree's Embedding, Image of a Projective variety. Dimension: Dimension of a Topological Space, Krull's Dimension, Dimension of the Intersection of a Variety with a hypersurface, Dimension and Morphisms. Local Properties.
Αffine Varieties - Projective varieties - Algebraic Varieties
Educational Material Types
  • Book
Course Organization
Reading Assigment
Written assigments
Student Assessment
Student Assessment methods
  • Written Exam with Short Answer Questions (Formative, Summative)
  • Oral Exams (Formative, Summative)
  • Written Exam with Problem Solving (Formative, Summative)
Course Bibliography (Eudoxus)
Δ. Πουλάκης, Αλγεβρική Γεωμετρία, Εκδόσεις Ζήτη, Θεσσαλονίκη 2018.
Additional bibliography for study
1. Dieudonné J. (1974) Cours de Géométrie Algébrique. PUF. 2. Fulton. W. (1978). Algebraic Curves. Benjamin. 3. Harris J. (1992). Algebraic Geometry. Springer Verlag. 4. Kendig K. (1977). Elementary Algebraic Geometry. Springer Verlag. 6. Mumford D. (1995) Algebraic Geometry I. Complex Projective Varieties. Springer Verlag. 7. Perrin D. (1995) Géométrie Algébrique. InterÉditions/Éditions CNRS. 8. Shafarevich I. R. (1994). Basic Algebraic Geometry. Springer Verlag. 9. Smith K. E., Kahanpää, Kekäläinen and Traves W. (2000). An Invitation to Algebraic Geometry. Springer Verlag. 10. Knuz E. (1985). Introduction to Commutative Algebra and Algebraic Geometry. Birkhäuser
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