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Introductory course in Algebraic Geometry

cours CIMPA

Tony EZOME

Summary:  I started by recalling the needed background from commutative algebra (noetherian modules and rings, finitely generated algebras, Hilbert basis theorem, integral/algebraic elements in a ring/field extension, transcendence degree of a field extension, the algebraic closure of a field) with useful exercice sessions. 

Then I introduced affine algebraic sets, the Zariski topology on the affine n-space and the Hilbert’s Nullstellensatz. I specified all these notions for the case of the affine line. I also introduced the coordinate ring of an affine algebraic set, its function fields, its dimension, smooth points (Jacoby criterion as well as a criterion using the maximal ideal of the localization). I did the same study for projective algebraic varieties. 

And then I introduced the decompostion into irreducible components. I also introduced homogenization and dehomogenization processes. I let student prove that any projective algebraic set is covered by a finite number of affine open subsets which are homeomorphic to closed subsets of an affine space. There were intensive exercice sessions.
 

Organizing institute
CIMPA
Institute
University of Bamenda
Country
Cameroun
City
Bambili
Level of the audience/possible candidates
Master or higher educational level
Type
cours CIMPA
Free cost event
Yes
Dates
-
Deadline

Procédure de candidature

Les cours CIMPA sont essentiellement destinés aux étudiants et étudiantes de l'institut d'accueil.