Geometry of Schemes (first part)
A.Y. 2021/2022
Learning objectives
The course provide an introduction to the general theory of schemes and their main properties.
Expected learning outcomes
The students will acquire some basic expertees that should allow them to approach some research subjects, such as the geometry of moduli spaces.
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 precise information about the delivery mode of the trainig activities for the academic year 2021/2022 will be provided over the next months, based on the evolution of the public health situation.
Course syllabus
The course aims at giving an introduction to the theory of schemes. A scheme is a vast algebraic generalization of the concept of topological variety and allows to deal with objects which are apparently very different. For example, the affine line over the complex numbers or (the spectrum) of the ring of integers Z are very similar from the point of view of schemes. We will introduce the notion of scheme, of sheaf on a scheme and of morphism of schemes with plenty of examples.
We will try to be as much as possible self-contained. In particular, we will recall the besic definitions and results from commutative algebra which are needed.
We will try to be as much as possible self-contained. In particular, we will recall the besic definitions and results from commutative algebra which are needed.
Prerequisites for admission
Commutative algebra. But this is not a compulsory prescription.
Teaching methods
Frontal lectures (in person or online).
Teaching Resources
R. Hartshorne, Algebraic geometry, Graduate Texts in Mathematics, No. 52. Springer-Verlag, New York-Heidelberg, 1977. xvi+496 pp.
Q. Liu, Algebraic geometry and arithmetic curves, Oxford Graduate Texts in Mathematics, 6. Oxford Science Publications. Oxford University Press, Oxford, 2002. xvi+576 pp.
Q. Liu, Algebraic geometry and arithmetic curves, Oxford Graduate Texts in Mathematics, 6. Oxford Science Publications. Oxford University Press, Oxford, 2002. xvi+576 pp.
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.
The final grade is expressed out of thirty and will be communicated to the student right after the oral exam.
Professor(s)
Reception:
Fix an appointment by email
Dipartimento di Matematica "F. Enriques" - Room 2046