Academic Year 2023-2024

HIGHER GEOMETRY

Teachers

Pietro De Poi
Unit Credits
6
Teaching Period
First Period
Course Type
Supplementary
Prerequisites. First two years of first-level degree in Mathematics
Teaching Methods. Lectures on blackboard. Homework which will be discussed before the lectures. Careful study at home by the student.
Verification of Learning. Written examination on exercises followed by an oral theoretical examination. Alternatively, oral examination and a final seminar on an argument—which presupposes the knowledge of the course—chosen by the student.

https://www.uniud.it/it/didattica/corsi/area-scientifica/scienze-matematiche-informatiche-multimediali-fisiche/laurea-magistrale/matematica/studiare/criteri-guida-di-assegnazione-del-voto-degli-esami-di-profitto/view

More Information. Oral examination by appointment also.

Other topics can be taught upon request.

The course could be held in English, upon proposal of the competent teaching structure.

Objectives
To understand basic complex geometry. To understand those basic topics of Riemann geometry useful to study the class of projective varieties. To use the language of differential forms and of vector bundles in the case of complex varieties.
Contents
We present some topics of Riemannian

Geometry, which can be formalized by the techniques of modern homological algebra. We introduce some abstract techniques used in modern research.

Texts
Simon Donaldson, Riemann surfaces. Oxford Graduate Texts in Mathematics, 22. Oxford University Press, Oxford, 2011. xiv+286 pp. ISBN: 978-0-19-960674-0

Rick Miranda

Algebraic Curves and Riemann Surfaces (Graduate Studies in Mathematics, Vol 5)