COURSE UNIT TITLE

: ELEMENTARY ALGEBRAIC GEOMETRY

Description of Individual Course Units

Course Unit Code Course Unit Title Type Of Course D U L ECTS
MAT 4043 ELEMENTARY ALGEBRAIC GEOMETRY ELECTIVE 4 0 0 7

Offered By

Mathematics

Level of Course Unit

First Cycle Programmes (Bachelor's Degree)

Course Coordinator

ASSISTANT PROFESSOR CELAL CEM SARIOĞLU

Offered to

Mathematics (Evening)
Mathematics

Course Objective

This course will introduce the basic objects in algebraic geometry: afine and projective varieties, and the maps between them. The focus will be on explicit concrete examples.

Learning Outcomes of the Course Unit

1   will be able to give the definitions of an affine and a projective varieties
2   Will be able to express the relation between algebraic varieties, ideals and coordinate rings in both affine and projective cases
3   will be able to calculate the singular points and the dimension of algebraic varieties
4   will be able to calculate the genus of a curve
5   will be able to resolve simple singularities via blow-ups

Mode of Delivery

Face -to- Face

Prerequisites and Co-requisites

None

Recomended Optional Programme Components

None

Course Contents

Week Subject Description
1 Affine and Projective spaces, Unit circle as a motivation for rational curves, rational curves, Conics and easy cases of Bézout s theorem
2 Cubics and the group law, Pascal s mystic hexagon, Curves and their genus
3 Noetherian rings, Hilbert basis theorem
4 Noether normalization, Zariski topology, Nullstelensatz
5 Regular functions and regular maps, product of affine varieties
6 Irreducible algebraic subsets, Rational functions, Rational maps, Birational maps
7 Projective variety, Projective Nullstellinsatz, Morphisms of projective varieties
8 Quadratics
9 Veronese varieties, Quasiprojective varieties and morphisms
10 Grassmannian variety, Product of varieties, Segre embedding
11 Nonsingular points of a hypersurface, Tangent space, Dimension
12 Dimension of intersection with a hypersurface, Blow-up in afine space, Blow-up in projective space
13 Resolution of singularities
14 Lines on surfaces

Recomended or Required Reading

1. Reid,M., Undergraduate Algebraic Geometry, Cambridge University Press, 1989, ISBN 978-0521356628
Supplementary Books:
2. Fulton, W., Algebraic Curves: an intr. to algebraic geometry, Addison Wesley, 1989, ISBN 978-0201510102
3. Shafarevich, I. R., Basic Alg Geo I, 2nd ed., Springer, 1994, ISBN 978-3540548126
4. Cox, D., Little, J., O shea D., Ideals, Varieties and Algorithms: an introduction to computational algebraic geometry and commutative algebra, 3rd ed., Springer, 2007, ISBN 978-0387356509
5. Gibson, C.G., Elementary Geometry of Algebraic Curves, Cambridge University Press, 1999, ISBN 978-0521641401
6. Brieskorn, E., Knörrer, H., Plane Algebraic Curves, Birkhauser, 1986, ISBN 978-3764317690
References:
7. Hartshorne, R. Algebraic Geometry, Springer, 1977, ISBN 978-0387902449
8. Eisenbud, D., Commutative Algebra with a View Toward Algebraic Geometry, Springer, 1995, 978-0387942698
9. Hauser, H.,Seven short stories on blow-ups and resolutions,International Press,

Planned Learning Activities and Teaching Methods

Lecture notes, presentation, problem solving, discussion.

Assessment Methods

SORTING NUMBER SHORT CODE LONG CODE FORMULA
1 MTE MIDTERM EXAM
2 QUZ QUIZ
3 ASG ASSIGNMENT
4 FIN FINAL EXAM
5 FCGR FINAL COURSE GRADE (RESIT) MTE * 0.30 + QUZ * 0.10 + ASG * 0.10 + FIN * 0.50
6 RST RESIT
7 FCGR FINAL COURSE GRADE (RESIT) MTE * 0.30 + QUZ * 0.10 + ASG * 0.10 + RST * 0.50


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

Further Notes About Assessment Methods

Quiz, Homework, Midterm, and Final exam

Assessment Criteria

30% (Midterm examination) +10%(Quiz)+10%(Assignment)+50% (Final examination).

Language of Instruction

English

Course Policies and Rules

The student is responsible for attending 70% of the courses throughout the semester. Action will be taken within the framework of the relevant regulations regarding unethical behavior that may occur in classes and exams. You can obtain the DEU Faculty of Science teaching and exam practice principles regulation from http://web.deu.edu.tr/fen.

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 4 56
Preparations before/after weekly lectures 13 3 39
Preparation for final exam 1 20 20
Preparation for quiz etc. 2 10 20
Preparation for midterm exam 1 15 15
Preparing assignments 2 10 20
Final 1 2 2
Midterm 1 2 2
Quiz etc. 2 1 2
TOTAL WORKLOAD (hours) 176

Contribution of Learning Outcomes to Programme Outcomes

PO/LOPO.1PO.2PO.3PO.4PO.5PO.6PO.7PO.8PO.9PO.10PO.11PO.12PO.13
LO.1544333343
LO.254433333
LO.354433333334
LO.45443333333
LO.5543333333