COURSE UNIT TITLE

: ALGEBRAIC CURVES

DEGREE PROGRAMMES

Description of Individual Course Units

Course Unit Code Course Unit Title Type Of Course D U L ECTS
MAT 5069 ALGEBRAIC CURVES ELECTIVE 3 0 0 7

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 purpose of this course is to introduce affine and projective curves and their properties, and so to make a concrete introduction to algebraic geometry.

Learning Outcomes of the Course Unit

1   will be able to write coordinate ring of an algebraic curve
2   will be able to calculate the intersection multiplicity of two algebraic curves
3   will be able to apply residue calculus to algebraic curves
4   will be able to calculate the genus of an algebraic curve
5   will be able to explain what is the Riemann-Roch theorem

Mode of Delivery

Face -to- Face

Prerequisites and Co-requisites

None

Recomended Optional Programme Components

None

Course Contents

Week Subject Description
1 Affine spcace; Affine Algebraic Curves
2 Projective space; Projective Algebraic curves
3 Coordinate ring of an algebraic curve
4 Rational functions on Algebraic curves
5 Intersection multiplicity and intersection cycle of two curves, Regular and singular points of algebraic curves, Tangents
6 Polars and Hessians of algebraic curves
7 The dual curve and the Plücker formulas
8 Midterm Examination
9 Elliptic Curves
10 The Residue Calculus
11 Applications of Residue theory to Curves
12 The Riemann-Roch Theorem
13 The genus of an Algebraic curve and of its Function field
14 The Canonical Divisor class, The branches of a curve singularity

Recomended or Required Reading

Textbook:
1. Ernst Kunz, Introduction to plane algebraic Curves, Birkhauser, 2005
Supplementary Books:
2. Gerd Fischer, Plane Algebraic Curves, American Mathematical Society, 2001
3. Makato Namba, Geometry of Projective Algebraic Curves, Marcel Dekker, 1984
References:
4. William Fulton, Algebraic Curves:An introduction to Algebraic Geometry, 1969
www.math.lsa.umich.edu/~wfulton/CurveBook.pdf
5. Rick Miranda, Algebraic Curves and Riemann Surfaces, American Mathematical Society, 1995
6. Frances Kirwan, Complex Algebraic Curves, London Mathematical Society, 1992.
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)

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

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 3 39
Preparation for midterm exam 1 26 26
Preparation for final exam 1 36 36
Preparing assignments 3 8 24
Final 1 3 3
Midterm 1 3 3
TOTAL WORKLOAD (hours) 170

Contribution of Learning Outcomes to Programme Outcomes

PO/LOPO.1PO.2PO.3PO.4PO.5PO.6PO.7PO.8PO.9PO.10PO.11
LO.1334334344
LO.23343334344
LO.334434434454
LO.434434434354
LO.54444444454

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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