Master's degree in Mathematics

Algebraic Geometry (2019/2020)

Course code
4S008272
Credits
6
Coordinator
Lidia Angeleri
Other available courses

Teaching is organised as follows:
Unit Credits Academic sector Period Academic staff
COMMUTATIVE ALGEBRA 3 MAT/02-ALGEBRA II semestre Lidia Angeleri
Ancora Da Definire
METHODS OF ALGEBRAIC GEOMETRY 3 MAT/03-GEOMETRY II semestre Lidia Angeleri
Ancora Da Definire

Learning outcomes

The goal of the course is to introduce the basic notions and techniques of algebraic geometry including the relevant parts of commutative algebra, and create a platform from which the students can take off towards more advanced topics, both theoretical and applied, also in view of a master's thesis project. The fist part of the course provides some basic concepts in commutative algebra, such as localization, Noetherian property and prime ideals. The second part covers fundamental notions and results about algebraic and projective varieties over algebraically closed fields and develops the theory of algebraic curves from the viewpoint of modern algebraic Geometry. Finally, the student will be able to deal with some applications, as for instance Gröbner basis or cryptosystems on elliptic curves over finite fields.

Syllabus

The fist part of the course provides some basic concepts in commutative algebra, such as localization, Noetherian property and prime ideals. The second part covers fundamental notions and results about algebraic and projective varieties over algebraically closed fields and develops the theory of algebraic curves from the viewpoint of modern algebraic Geometry.

Assessment methods and criteria

The exam consists of a written examination. The mark obtained in the written examination can be improved by the mark obtained for the homework and/or by an optional oral examination. Only students who have passed the written exam will be admitted to the oral examination.

Reference books
Author Title Publisher Year ISBN Note
Sigfried Bosch Algebraic Geometry and Commutative Algebra Springer  
David Eisenbud Commutative Algebra: with a View Toward Algebraic Geometry Springer  




© 2002 - 2019  Verona University
Via dell'Artigliere 8, 37129 Verona  |  P. I.V.A. 01541040232  |  C. FISCALE 93009870234