Studying at the University of Verona
Here you can find information on the organisational aspects of the Programme, lecture timetables, learning activities and useful contact details for your time at the University, from enrolment to graduation.
Study Plan
This information is intended exclusively for students already enrolled in this course.If you are a new student interested in enrolling, you can find information about the course of study on the course page:
Laurea magistrale in Mathematics - Enrollment from 2025/2026The Study Plan includes all modules, teaching and learning activities that each student will need to undertake during their time at the University.
Please select your Study Plan based on your enrollment year.
1° Year
| Modules | Credits | TAF | SSD |
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| Modules | Credits | TAF | SSD |
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| Modules | Credits | TAF | SSD |
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1 module between the following1 module between the following3 modules among the followingLegend | Type of training activity (TTA)
TAF (Type of Educational Activity) All courses and activities are classified into different types of educational activities, indicated by a letter.
Algebraic Geometry (2019/2020)
Teaching code
4S008272
Credits
6
Coordinator
Language
English
Also offered in courses:
- Algebraic geometry (seminar course) of the course Master's degree in Mathematics
The teaching is organized as follows:
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.
Program
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.
Bibliography
| Author | Title | Publishing house | Year | ISBN | Notes |
|---|---|---|---|---|---|
| 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 |
Examination Methods
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.
