COURSE UNIT TITLE

: ALGEBRAIC SURFACES

Description of Individual Course Units

Course Unit Code Course Unit Title Type Of Course D U L ECTS
MAT 5073 ALGEBRAIC SURFACES 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 introduce the classification of algebraic surfaces (mainly Enriques-Castelnuovo's classification for characteristic zero and Bombieri-Mumford classification for characteristic p) .

Learning Outcomes of the Course Unit

1   will be able to know ruled surfaces and their properties
2   will be able to know K3 surfaces and their properties
3   will be able to know Enriques and Castelnuovo s classification of algebraic surfaces in chracteristic zero
4   will be able to know Bombieri-Mumford s classification of algebraic surfaces in characteristic p
5   will be able to classify the surfaces with respect to their Kodaira dimension

Mode of Delivery

Face -to- Face

Prerequisites and Co-requisites

None

Recomended Optional Programme Components

None

Course Contents

Week Subject Description
1 Linear, algebraic and numerical equivalence of divisors
2 Birational maps between surfaces
3 Ruled surfaces, Rational surfaces
4 Linear systems, Rational normal scrolls
5 Castelnuovo's criterion for rationality
6 Picard s variety
7 Albenese Variety
8 Non-ruled and Ruled surfaces
9 Classification of Ruled surfaces
10 Elliptic and quasi-elliptic surfaces, Kodaira dimension
11 K3 surfaces
12 Enrique Surfaces
13 Fibrations
14 Classification and Moduli

Recomended or Required Reading

Textbooks:
1. Lucian Badescu, Algebraic Surfaces, Springer, 2001
2. W. P. Barth, K. Hulek, C.A.M.Peters, A. Van de Ven, Compact Complex Surfaces, 2nd ed. Springer, 2004
3. Phillip Griffiths, Joe Harris, Principles of Algebraic Geometry, Wiley-Interscience, 1994 (chapter4)
Supplementary Books:
4. O. Zariski, S.S. Abhyankar, J. Lipmann, D. Mumford, Algebraic Surfaces, Springer, 2nd ed., 1971
5. David Mumford, Lectures on Curves on an Algebraic Surface, Princeton University Press, 1966
6. Robin Hartshorne, Algebraic Geometry, Springer, 1997 (chapter5)
7. Miles Reid, Chapters on algebraic surfaces, arXiv:alg-geom/9602006v1, 1996
8. Christian Liedtke, Algebraic Surfaces in positive characteristic, arXiv:0912.4291 v4 [math.AG], 2013
References:
9. E. Bombieri, D. Mumford, Classification of surfaces in characteristic p, III; Inventh. Math. 35 (1976): 197 - 232
10. K. Kodaira, On compact Analytic Surfaces I, Ann. of Math. 71 (1960): 111-152
11. K. Kodaira, On compact Analytic Surfaces II, Ann. of Math. 77 (1963): 563 626
12. K. Kodaira, On compact Analytic Surfaces III, Ann. of Math. 78 (1963): 1-40
13. David Mumford, Enriques classification of Surfaces in characteristic p, I; Global Analysis: papers in honors of K. Kodaira, Edited by Donald Clayton and Shokichi Iyanga, Princeton University Press, 1969, pp: 325-339.
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/LOPO.1PO.2PO.3PO.4PO.5PO.6PO.7PO.8PO.9PO.10PO.11
LO.133344323443
LO.244344323443
LO.344344222443
LO.444344222443
LO.544344223443