# 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

Mathematics
Mathematics

#### 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

Face -to- Face

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#### 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 Midterm 9 Non-ruled and Ruled surfaces, classification of Ruled surfaces 10 Elliptic and quasi-elliptic surfaces, Kodaira dimension 11 K3 surfaces 12 Enrique Surfaces 13 Fibrations 14 Classification and Moduli

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

#### Assessment Methods

 SORTING NUMBER SHORT CODE LONG CODE FORMULA 1 ASG ASSIGNMENT 2 MTE MIDTERM EXAM 3 PRJ PROJECT 4 FCG FINAL COURSE GRADE ASG * 0.30 + MTE * 0.40 + PRJ * 0.30

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

None

To be announced.

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: +90 232 301 8607

To be announced.

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