• Basic information
• Learning outcomes
• Contents
• Assessment
• Workload

Learning outcomes

Upon successful completion of this course, students will be able to:

1. Understand the notion of algebraic varieties and morphisms

   Contribution to Program Outcomes

   1. Define and manipulate advanced concepts of Mathematics in a specialized way
   2. Gain original, independent and critical thinking, and develop theoretical concepts and tools,
   3. Understand relevant research methodologies and techniques and their appropriate application within his/her research field,

   Method of assessment

   1. Written exam
   2. Homework assignment
2. Understand the notion of singularity on algebraic varieties and curves

   Contribution to Program Outcomes

   1. Define and manipulate advanced concepts of Mathematics in a specialized way
   2. Understand relevant research methodologies and techniques and their appropriate application within his/her research field,
   3. Acquire scientific knowledge and work independently,
   4. Effectively express his/her research ideas and findings both orally and in writing

   Method of assessment

   1. Written exam
   2. Homework assignment
3. Gain a knowledge on shevaes and schemes required to pursue advanced studies on modern algebraic geometry

   Contribution to Program Outcomes

   1. Define and manipulate advanced concepts of Mathematics in a specialized way
   2. Gain original, independent and critical thinking, and develop theoretical concepts and tools,
   3. Understand relevant research methodologies and techniques and their appropriate application within his/her research field,
   4. Acquire scientific knowledge and work independently,
   5. Effectively express his/her research ideas and findings both orally and in writing

   Method of assessment

   1. Written exam
   2. Homework assignment

Contents
Week 1:	Affine algebraic sets; affine spaces and algebraic sets, the ideal of a set of points, Hilbert Basis Theorem, irreducibility
Week 2:	Affine algebraic sets; Hilbert's Nulstellensatz, finitines conditions on mudules, field extensions
Week 3:	Affine varieties; affine coordinate ring, Zariski Topology
Week 4:	Dimension of an affine variety, projective spaces
Week 5:	Projective varieties; graded rings and homogenous coordinate ring, covering of projective varieties by affine varieties
Week 6:	Regular functions and morphisms on varieties, local rings
Week 7:	Rational maps on varieties, birational maps
Week 8:	Singularity, nonsingular varieties
Week 9:	Discrete valuation rings, nonsingular curves
Week 10:	Projective plane curves, Bezout's Theorem
Week 11:	Intersection in projective spaces, degree of a variety
Week 12:	Sheaves of abelian groups, direct image and inverse image sheaves
Week 13:	Affine schemes; prime spectrum of a ring, Zariski topology on prime spectrums,
Week 14:	Schemes; glueing sheaves and schemes, relation between the category of varieties and the category of schemes
Week 15*:	-
Week 16*:	Final Exam.
Textbooks and materials:	Algebraic Geometry, Robin Hartshorne, Springer-Verlag, 1977
Recommended readings:	1. Algebraic Curves: An Introduction to Algebraic Geometry, William Fulton, Addison-Wesley, 1969 2. Algebraic Geometry 1: From Algebraic Varieties to Schemes (Translations of Mathematical Monographs), Kenji Ueno, American Mathematical Society, 1999
	* Between 15th and 16th weeks is there a free week for students to prepare for final exam.

Assessment
Method of assessment	Week number	Weight (%)
Mid-terms:		0
Other in-term studies:		0
Project:		0
Homework:	2, 4, 5, 6, 7, 9, 11, 12, 14	40
Quiz:		0
Final exam:	16	60
	Total weight:	(%)

Workload
Activity	Duration (Hours per week)	Total number of weeks	Total hours in term
Courses (Face-to-face teaching):	3	14
Own studies outside class:	5	14
Practice, Recitation:	0	0
Homework:	6	9
Term project:	0	0
Term project presentation:	0	0
Quiz:	0	0
Own study for mid-term exam:	0	0
Mid-term:	0	0
Personal studies for final exam:	20	1
Final exam:	3	1
		Total workload:
		Total ECTS credits:	*
	* ECTS credit is calculated by dividing total workload by 25. (1 ECTS = 25 work hours)