Algebraic Geometry (ΓΕ7): Διαφορά μεταξύ των αναθεωρήσεων
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(Νέα σελίδα με 'Graduate Courses Outlines - [https://math.uoi.gr Department of Mathematics] === General === {| class="wikitable" |- ! School | School of Science |- ! Academic Unit | Department of Mathematics |- ! Level of Studies | Graduate |- ! Course Code | ΧΧΧ |- ! Semester | 000 |- ! Course Title | ΧΧΧ |- ! Independent Teaching Activities | Lectures (Weekly Teaching Hours: 3, Credits: 7.5) |- ! Course Type | General Background |- ! Prerequisite Courses | - |- ! L...') |
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=== General === | === General === | ||
| Γραμμή 15: | Γραμμή 17: | ||
|- | |- | ||
! Course Code | ! Course Code | ||
| | | ΓΕ7 | ||
|- | |- | ||
! Semester | ! Semester | ||
| | | 2 | ||
|- | |- | ||
! Course Title | ! Course Title | ||
| | | Algebraic Geometry | ||
|- | |- | ||
! Independent Teaching Activities | ! Independent Teaching Activities | ||
| Γραμμή 27: | Γραμμή 29: | ||
|- | |- | ||
! Course Type | ! Course Type | ||
| | | Special Background | ||
|- | |- | ||
! Prerequisite Courses | ! Prerequisite Courses | ||
| Γραμμή 34: | Γραμμή 36: | ||
! Language of Instruction and Examinations | ! Language of Instruction and Examinations | ||
| | | | ||
Greek | |||
|- | |- | ||
! Is the Course Offered to Erasmus Students | ! Is the Course Offered to Erasmus Students | ||
| Yes | | Yes (in English) | ||
|- | |- | ||
! Course Website (URL) | ! Course Website (URL) | ||
| Γραμμή 49: | Γραμμή 51: | ||
! 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 | ! General Competences | ||
| | | | ||
The aim of the course is to empower the postgraduate student to analyse and compose advanced notions of Algebraic Geometry. | |||
|} | |} | ||
=== Syllabus === | === 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 === | === Teaching and Learning Methods - Evaluation === | ||
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! Delivery | ! Delivery | ||
| | | | ||
Face-to-face | |||
|- | |- | ||
! Use of Information and Communications Technology | ! Use of Information and Communications Technology | ||
| | | - | ||
|- | |- | ||
! Teaching Methods | ! Teaching Methods | ||
| Γραμμή 81: | Γραμμή 82: | ||
| 39 | | 39 | ||
|- | |- | ||
| | | Study of theory | ||
| | | 78 | ||
|- | |- | ||
| | | Solving of exercises | ||
| | | 70.5 | ||
|- | |- | ||
| Course total | | Course total | ||
| Γραμμή 93: | Γραμμή 94: | ||
! Student Performance Evaluation | ! Student Performance Evaluation | ||
| | | | ||
Written exam at the end of semester (obligatory), problem solving or/and intermediate exams (optional). | |||
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Τελευταία αναθεώρηση της 16:28, 15 Ιουνίου 2023
- Ελληνική Έκδοση
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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 |
| ||||||||||
| 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.