Projective Algebraic Geometry
A.Y. 2026/2027
Learning objectives
The aim of the course is to give an introduction to affine and projective algebraic varieties.
Expected learning outcomes
Knowledge of some elementary properties of affine and projective algebraic varieties and ability to use them in some concrete instances.
Lesson period: First semester
Assessment methods: Esame
Assessment result: voto verbalizzato in trentesimi
Single course
This course cannot be attended as a single course. Please check our list of single courses to find the ones available for enrolment.
Course syllabus and organization
Single session
Responsible
Lesson period
First semester
Course syllabus
Affine and projective varieties, grassmannians, birational maps, tangent space, singularities, Hilbert polynomial, degree of a variety, elliptic curves, divisors on curves
Prerequisites for admission
Groups, rings and fields, linear algebra, affine and projective spaces. General topology. Required results in commutative algebra will be recalled during the course.
Teaching methods
Lectures in classroom
Teaching Resources
I. R. Shafarevich, Basic Algebraic Geometry 1, Springer
R. Hartshone, Algebraic Geometry, Springer
D. Mumford, Algebraic Geometry 1, Complex Projective varieties, Springer
J. Harris, Algebraic Geometry: A first course, Springer
Notes on the web:
Andreas Gathmann, Algebraic Geometry
Ben Moonen, Introduction to algebraic geometry
R. Hartshone, Algebraic Geometry, Springer
D. Mumford, Algebraic Geometry 1, Complex Projective varieties, Springer
J. Harris, Algebraic Geometry: A first course, Springer
Notes on the web:
Andreas Gathmann, Algebraic Geometry
Ben Moonen, Introduction to algebraic geometry
Assessment methods and Criteria
Oral exam concerning the topics of the course and discussion of some exercises which will be assigned weekly during the semester. The exercises should be submitted to the instructor before the oral exam.
MATH-02/B - Geometry - University credits: 6
Exercises: 12 hours
Lessons: 35 hours
Lessons: 35 hours
Professor:
Lombardi Luigi
Professor(s)
Reception:
Thursday 4:20pm-5:20pm or by appointment
Math Department in via C. Saldini 50. Office: 1.109