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 5071	ALGEBRAIC GEOMETRY I	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

Algebraic geometry is a multi-discipliner science and have become a popular for the last 50 years. It aims to find a solutions to geometric problems by using algebraic techniques and also find solutions to algebraic problems by using geometric techniques.

The aim of this course is to serve as an introduction to classical algebraic geometry, and make the students familiar with concepts and techniques of algebraic geometry.

Learning Outcomes of the Course Unit

1	will be able to describe local properties of algebraic varieties.
2	will be able to determine singular points of an algebraic variety.
3	will be able to apply blow-up to a singular point.
4	will be able to write divisors of a variety.
5	will be able to Apply the Riemann-Roch theorem to algebraic curves.

Mode of Delivery

Face -to- Face

Prerequisites and Co-requisites

None

Recomended Optional Programme Components

None

Course Contents

Week	Subject	Description
1	Algebraic curves in the plane; Closed subsets of Affine Space
2	Rational Functions; Quasi-projective Varieties
3	Products and maps of Quasi-projective varieties
4	Dimension, Singular and Non-singular points
5	Power series expansions, Properties of Non-singular points
6	Blow-up
7	Normal Varieties; Singularitites of a map
8	Midterm Examination
9	Divisors; Divisors on curves
10	The plane cubic; Algebraic groups
11	Differential Forms
12	Applications of Differential Forms
13	Intersection Numbers, The Riemann-Roch Theorem
14	Singularities

Recomended or Required Reading

Textbooks:
1. Igor R. Shafarevich, Basic Algebraic Geometry 1: Varieties in Projective Space, Springer, 2nd ed., 1994
2. Robin Hartshorne, Algebraic Geometry, Springer, 1997
Supplementary Books:
3. William Fulton, Algebraic Curves:An introduction to Algebraic Geometry, 1969
It's 2008 edition is avilable at the webpage: www.math.lsa.umich.edu/~wfulton/CurveBook.pdf
4. Ernst Kunz, Introduction to Commutative Algebra and Algebraic Geometry, Birkhauser, 1984
References:
5. Igor R. Shafarevich, Basic Algebraic Geometry 2: Schemes and Complex Manifolds, Springer, 2nd ed., 1996
6. Joe Harris, Algebraic Geometry: a first course, Springer 1995
7. Phillip Griffiths, Joe Harris, Principles of Algebraic Geometry, Wiley-Interscience, 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 3018607

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/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	4	4	3	4	3	3	4	4	3
LO.2	3	3	4	4	3	4	3	3	4	4	3
LO.3	3	3	4	4	4	4	3	3	4	4	3
LO.4	4	4	4	4	4	4	3	3	4	4	3
LO.5	4	4	4	4	4	4	3	3	4	4	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