Dokuz Eylül University Information Package / Courses Catalog

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 (English)
Mathematics (English)

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	Classification of Geometric objects and Universal Schemes
9	The Topology of Algebraic Curves
10	Complex Manifolds
11	Divisors and Meromorphic functions
12	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, discussion.

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

Further Notes About Assessment Methods

None

Assessment Criteria

30% (Midterm examination) +30%(Homework assignment)+40% (Final examination)

Language of Instruction

English

Course Policies and Rules

Attending at least 70 percent of lectures is mandatory.

Contact Details for the Lecturer(s)

Asst. Prof. Dr. Celal Cem SARIOĞLU
E-mail: celalcem.sarioglu@deu.edu.tr
Phone: +90 232 301 8585
Office: B212 (Mathematics Department)

Office Hours

To be announced later.

Work Placement(s)

None

Workload Calculation

Activities	Number	Time (hours)	Total Work Load (hours)
Lectures	14	3	42
Preparations before/after weekly lectures	13	3	39
Preparation for midterm exam	1	25	25
Preparation for final exam	1	30	30
Preparing assignments	6	8	48
Final	1	3	3
Midterm	1	3	3
TOTAL WORKLOAD (hours)			190

Contribution of Learning Outcomes to Programme Outcomes

PO/LO	PO.1	PO.2	PO.3	PO.4	PO.5	PO.6	PO.7	PO.8	PO.9	PO.10	PO.11
LO.1	3	3	3	4	4	4	3	4	4	5	3
LO.2	4	4	4	5	4	4	3	4	4	5	3
LO.3	4	4	4	5	4	4	3	4	4	5	3
LO.4	4	4	4	5	4	4	3	4	4	5	3
LO.5	4	4	4	5	4	4	3	4	4	5	3

COURSE UNIT TITLE

DEGREE PROGRAMMES

Description of Individual Course Units

Offered By

Level of Course Unit

Course Coordinator

Offered to

Course Objective

Learning Outcomes of the Course Unit

Mode of Delivery

Prerequisites and Co-requisites

Recomended Optional Programme Components

Course Contents

Recomended or Required Reading

Planned Learning Activities and Teaching Methods

Assessment Methods

Further Notes About Assessment Methods

Assessment Criteria

Language of Instruction

Course Policies and Rules

Contact Details for the Lecturer(s)

Office Hours

Work Placement(s)

Workload Calculation

Contribution of Learning Outcomes to Programme Outcomes

CONTACT INFORMATION