M211 (Algebraic Geometry)
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2015–2016
MATHM211
Masters
Half unit (= 7.5 ECTS credits)
1
3 hour lectures per week
90% examination, 10% coursework
MATH3201, MATH3202
Dr L Guerberoff
Course Description and Objectives
Algebraic Geometry is the study of algebraic sets (or varieties), all those defined by polynomial
equations in several variables. Although the subject probably goes back to Descartes, it is still
one of the most thriving research areas of pure mathematics. In addition, Algebraic Geometry
is connected to many other areas of mathematics such as number theory for example.
Our aim is to introduce basic notions of algebraic geometry in the most down-to-earth fashion.
After defining affine and projective algebraic sets and studying their basic properties, we will
mostly focus on the case of algebraic curves. One of the main aims of the course is to prove the
Bezout’s theorem about intersection of two plane projective curves.
Recommended Texts
Recommended book is W. Fulton, Algebraic curves.
Detailed Syllabus
− Affine algebraic sets: definitions, basic properties, Hilbert’s Nullstellensatz, coordinate
rings, rational functions, local rings.
− Local properties of plane algebraic curves.
− Projective algebraic sets, Bezout’s theorem.
− If time permits, Riemann Roch Theorem.
April 2015 MATHM211