Algebraic Geometry (ΓΕ7)

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General

School	School of Science
Academic Unit	Department of Mathematics
Level of Studies	Graduate
Course Code	ΓΕ7
Semester	2
Course Title	Algebraic Geometry
Independent Teaching Activities	Lectures (Weekly Teaching Hours: 3, Credits: 7.5)
Course Type	Special Background
Prerequisite Courses	-
Language of Instruction and Examinations	Greek
Is the Course Offered to Erasmus Students	Yes (in English)
Course Website (URL)	See eCourse, the Learning Management System maintained by the University of Ioannina.

Learning Outcomes

Learning outcomes	The aim of the course is the postgraduate student to reach a good level of theoretical background on topics related to the algebraic geormetry.
General Competences	The aim of the course is to empower the postgraduate student to analyse and compose advanced notions of Algebraic Geometry.

Syllabus

Affine Varieties, Nullstellensatz, dimension, Regular and rational functions on Varieties, Projective varieties, birational geometry, tangent space and nonsingularity, divisors, differential forms, canonical class, Riemann-Roch theorem.

Teaching and Learning Methods - Evaluation

Delivery	Face-to-face
Use of Information and Communications Technology	-
Teaching Methods	Activity Semester Workload Lectures 39 Study of theory 78 Solving of exercises 70.5 Course total 187.5
Student Performance Evaluation	Written exam at the end of semester (obligatory), problem solving or/and intermediate exams (optional).

Attached Bibliography

• Shafarevich, Igor R. Basic algebraic geometry 1, Varieties in Projective Space, Springer, 2013.
• Shafarevich, Igor R. Basic algebraic geometry 2, Schemes and Complex Manifolds, Springer, 2013.