| Unit | Credits | Academic sector | Period | Academic staff |
|---|---|---|---|---|
| COMMUTATIVE ALGEBRA | 3 | MAT/02-ALGEBRA | II semestre |
Lidia Angeleri
Rosanna Laking |
| METHODS OF ALGEBRAIC GEOMETRY | 3 | MAT/03-GEOMETRY | II semestre |
Lidia Angeleri
Rosanna Laking |
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.
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.
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.
| 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 |
