ALGEBRAIC GEOMETRY

Course objectives

General goals. To acquire basic notions and skills in algebraic geometry. Specific goals. Knowledge and comprehension: at the end of the course the student will have learnt basic notions and results on affine and projective varieties, quasi-projective varieties, dimension, and first local/global properties. Applied knowledge and comprehension: at the end of the course the student will the skill to go into and appreciate modern algebraic geometry. Critical development: the student will appreciate the interaction between different fields such as commutative algebra, complex analysis, analytic and projective geometry. Communication skills: the ability to make a clear presentation of parts of the theory introduced in the course. Learning skills: the knowledge acquired will be useful in studying more specialized courses in algebraic and complex geometry.

Channel 1
FABIO BERNASCONI Lecturers' profile

Program - Frequency - Exams

Course program
Algebraic varieties: definition of affine varieties, Hilbert's theorems, projective and quasi-projective varieties. Vector bundles on algebraic varieties. Morphisms of algebraic varieties. Dimension theory. Regularity, smoothness, and local notions of singularities for algebraic varieties. Algebraic curves and the Riemann-Roch theorem.
Prerequisites
Complex analysis, topology and commutative algebra.
Books
Note del docente. Shafarevich, Algebraic geometry
Frequency
Not mandatory.
Exam mode
A written test with basic algebraic geometry exercises. If the written test is satisfactory, the student will be required to take an oral exam covering the entire course syllabus.
Lesson mode
In presence lecture.
  • Lesson code1031361
  • Academic year2025/2026
  • CourseMathematics
  • CurriculumAlgebra e Geometria
  • Year1st year
  • Semester2nd semester
  • SSDMAT/03
  • CFU6