Geometria degli schemi
A.Y. 2025/2026
Learning objectives
The course provides an introduction to the general theory of schemes
and their main properties. In the advanced part, we expose the
students to some advanced topics including coherent and quasi-coherent
sheaves and some rudiments of birational geometry
and their main properties. In the advanced part, we expose the
students to some advanced topics including coherent and quasi-coherent
sheaves and some rudiments of birational geometry
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.
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 can be attended as a single course.
Course syllabus and organization
Single session
Responsible
Course syllabus
The first part (6 cfu) 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 notions of scheme, of sheaf on a scheme and of morphism of schemes with plenty of examples. We will then study the cohomology of a sheaf on a scheme and its main properties.
Prerequisites for admission
Non sono presenti prerequisiti.
Teaching methods
Frontal lectures.
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 consists of an oral exam during which the student will be asked to illustrate some contents of the program of the course in order to evaluate her/his understanding of the contents of the course and her/his ability in applying them by solving some exercises.
MAT/03 - GEOMETRY - University credits: 6
Practicals: 12 hours
Lessons: 35 hours
Lessons: 35 hours
Professors:
Pertusi Laura, Stellari Paolo
Professor(s)
Reception:
Fix an appointment by email
Dipartimento di Matematica "F. Enriques" - Room 2046