COURSE UNIT TITLE

: ALGEBRAIC GEOMETRY II

DEGREE PROGRAMMES

Description of Individual Course Units

Course Unit Code Course Unit Title Type Of Course D U L ECTS
MAT 5062 ALGEBRAIC GEOMETRY II ELECTIVE 3 0 0 8

Offered By

Graduate School of Natural and Applied Sciences

Level of Course Unit

Second Cycle Programmes (Master's Degree)

Course Coordinator

ASSISTANT PROFESSOR CELAL CEM SARIOĞLU

Offered to

Mathematics
Mathematics

Course Objective

The aim of this course is to study algebraic geometry from the modern point of view, and make the students familiar with concepts and techniques of modern algebraic geometry.

Learning Outcomes of the Course Unit

1   will be able to describe Spectrum of a ring
2   will be able to use schemes to study geometry
3   will be able to describe fundamental properties of sheaves on schemes
4   will be able to describe the topology of algebraic curves
5   will be able to find a uniformization of algebraic curves

Mode of Delivery

Face -to- Face

Prerequisites and Co-requisites

None

Recomended Optional Programme Components

None

Course Contents

Week Subject Description
1 The Spec of a Ring
2 Presheaves and Sheaves
3 Schemes
4 Products of Schemes
5 Vector bundles and Sheaves
6 Coherent Sheaves
7 Cohomology of Coherent Sheaves
8 Midterm
9 Classification of Geometric objects and Universal Schemes
10 The Topology of Algebraic Curves
11 Complex Manifolds
12 Divisors and Meromorphic functions, Kahler manifolds
13 The uniformization of algebraic curves and Riemann surfaces
14 Uniformization of higher dimensional varieties

Recomended or Required Reading

Textbooks:
1. Igor R. Shafarevich, Basic Algebraic Geometry 2: Schemes and Complex Manifolds, Springer, 2nd ed., 1996
2. Robin Hartshorne, Algebraic Geometry, Springer, 1997
3. David Mumford, E. Arbarello, The red book of Varieties and Schemes, Springer, 2nd ed., 1999
Supplementary Books:
4. David Eisenbud, Joe Harris, The Geometry of Schemes, Springer, 2001
5. Kenji Ueno, Algebraic Geometry 1: from algebraic Varieties to Schemes, AMS, 1995
6. Kenji Ueno, Algebraic Geometry 2: Sheaves and Cohomology, AMS, 2001
References:
7. Kenji Ueno, Algebraic Geometry 3: Further study of Schemes, AMS, 2003
8. Joe Harris, Algebraic Geometry: a first course, Springer 1995
9. Phillip Griffiths, Joe Haris, Principles of Algebraic Geometry, Wiley-Interscience, 1994
10. Igor R. Shafarevich, Basic Algebraic Geometry 1: Varieties in Projective Space, Springer, 2nd ed., 1994
Materials:

Planned Learning Activities and Teaching Methods

Lecture notes, Presentation, Problem solving

Assessment Methods

SORTING NUMBER SHORT CODE LONG CODE FORMULA
1 ASG ASSIGNMENT
2 MTE MIDTERM EXAM
3 FIN FINAL EXAM
4 FCG FINAL COURSE GRADE ASG * 0.30 + MTE * 0.30 + FIN * 0.40
5 RST RESIT
6 FCGR FINAL COURSE GRADE (RESIT) ASG * 0.30 + MTE * 0.30 + RST * 0.40


*** Resit Exam is Not Administered in Institutions Where Resit is not Applicable.

Further Notes About Assessment Methods

None

Assessment Criteria

To be announced.

Language of Instruction

English

Course Policies and Rules

Attending at least 70 percent of lectures is mandatory.

Contact Details for the Lecturer(s)

E-mail: celalcem.sarioglu@deu.edu.tr
Office Phone: +90 232 301 8607

Office Hours

To be announced.

Work Placement(s)

None

Workload Calculation

Activities Number Time (hours) Total Work Load (hours)
Lectures 13 3 39
Preparations before/after weekly lectures 13 4 52
Preparation for midterm exam 1 23 23
Preparation for final exam 1 30 30
Preparing assignments 8 6 48
Final 1 3 3
Midterm 1 3 3
TOTAL WORKLOAD (hours) 198

Contribution of Learning Outcomes to Programme Outcomes

PO/LOPO.1PO.2PO.3PO.4PO.5PO.6PO.7PO.8PO.9PO.10PO.11
LO.133344434453
LO.244454434453
LO.344454434453
LO.444454434453
LO.544454434453

CONTACT INFORMATION
Dokuz Eylül Üniversitesi Cumhuriyet Bulvarı No: 144 35210 Alsancak / İZMİR
Phone: +90(232) 412 12 12 - Fax: +90 (232) 464 81 35

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