Projective Algebraic Geometry
A.Y. 2021/2022
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
More specific information on the delivery modes of training activities for academic year 2021/22 will be provided over the coming months, based on the evolution of the public health situation
Course syllabus
Affine algebraic varieties, affine space, Hilbert's Nullstellensatz, hyperplanes, conics, Zariski's topology, dimensions, regular functions and maps between algebraic varieties, rational and birational maps, projective algebraic varieties, projective space, birational equivalence, abstract varieties, sheaves, line bundles, vector bundles, tangent spaces, smoothness, blow-ups, resolution of singularities, Hilbert polynomials, Grassmannians, Segre and Veronese embeddings, Bezout's theorem, enumerative geometry, examples.
Prerequisites for admission
A basic knowledge of commutative algebra is recommended
Teaching methods
Lectures
Teaching Resources
A. Gathmann: Algebraic Geometry, Class Notes TU Kaiserslautern 2019/20.
R. Hartshorne: Introduction to Algebraic Geometry, Springer-Verlag 1977.
I. R. Shafarevich: Basic Algebraic Geometry I, Springer-Verlag 1977.
R. Hartshorne: Introduction to Algebraic Geometry, Springer-Verlag 1977.
I. R. Shafarevich: Basic Algebraic Geometry I, Springer-Verlag 1977.
Assessment methods and Criteria
The exam is oral. During the exam, the student will be asked to
illustrate some of the contents of the course to evaluate her/his
knowledge and comprehension of the topics treated during the course
and her/his ability to apply them.
The final grade is expressed out of thirty and will be communicated to
the student right after the oral exam.
illustrate some of the contents of the course to evaluate her/his
knowledge and comprehension of the topics treated during the course
and her/his ability to apply them.
The final grade is expressed out of thirty and will be communicated to
the student right after the oral exam.
Professor(s)