Algebraic Geometry (2019/2020)

Course code
4S008272
Name of lecturer
Lidia Angeleri
Coordinator
Lidia Angeleri
Number of ECTS credits allocated
6
Language of instruction
English
Location
VERONA
Period
not yet allocated

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.

Reference books
Author Title Publisher Year ISBN Note
William Fulton Algebraic Curves. An Introduction to Algebraic Geometry. Addison-Wesley 2008
Sigfried Bosch Algebraic Geometry and Commutative Algebra Springer 2013
David Eisenbud Commutative Algebra: with a View Toward Algebraic Geometry Springer 2011
Klaus Hulek Elementary Algebraic Geometry AmericanMathematical Society 2003
Ernst Kunz Introduction to Commutative Algebra and Algebraic Geometry, Birkhäuser, Springer 2013

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.