Academic Year 2021-2022



Pietro De Poi
Unit Credits
Teaching Period
First Period
Course Type
Prerequisites. First two years of first-level degree in Mathematics
Teaching Methods. Lectures.
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.
More Information. Oral examination by appointment. Other topics can be taught upon request.

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

The student will have to:

Knowledge and understanding: To know some basic concepts and results of the course. To know some modern problems of algebraic geometry, recognizing their difficulty. To know how to use the modern language in formulating algebraic geometry problems.

Ability to apply knowledge and understanding: To know how to deal with and solve with modern or elementary language some classical problems of algebraic geometry. To find relationships between issues of algebraic geometry and problems or theories in different fields. To know how to solve problems beyond those discussed during the course Independent thinking: To know how to find the most appropriate analytical, algebraic, or geometric techniques in solving assigned problems. To address the difficulty of specific problems in algebraic geometry.

Communication skills: To introduce, orally and in writing, a subject, or a mathematical theory, learned during the course. Being able to present to a non-specialist public the salient aspects of classical theory and some modern problem of projective algebraic geometry.

Learning ability: to be able to read a research paper in the fields covered by the course. To work independently in literature search. To address the proposed problems by selecting independently the most meaningful ones.

The aim of the course is to deepen some specific aspects of contemporary Algebraic Geometry such a knowledge of the elementary thecniques of the theory of schemes, or the theory of rational surfaces, or the theory of abelian varieties or some specific aspects of the theory of the curves.
Hartshorne, Robin, Algebraic geometry. Graduate Texts in Mathematics, No. 52. Springer-Verlag, New York-Heidelberg, 1977. xvi+496 pp. ISBN: 0-387-90244-9

Iitaka, Shigeru, Algebraic geometry. An introduction to birational geometry of algebraic varieties. Graduate Texts in Mathematics, 76. North-Holland Mathematical Library, 24. Springer-Verlag, New York-Berlin, 1982. x+357 pp. ISBN: 0-387-90546-4

Shafarevich, Igor R., Basic algebraic geometry. 2. Schemes and complex manifolds. Third edition. Translated from the 2007 third Russian edition by Miles Reid. Springer, Heidelberg, 2013. xiv+262 pp. ISBN: 978-3-642-38009-9; 978-3-642-38010-5

Arbarello, E.; Cornalba, M.; Griffiths, P. A.; Harris, J. Geometry of algebraic curves. Vol. I. Grundlehren der Mathematischen Wissenschaften [Fundamental Principles of Mathematical Sciences], 267. Springer-Verlag, New York, 1985. xvi+386 pp. ISBN: 0-387-90997-4

Birkenhake, Christina; Lange, Herbert, Complex abelian varieties. Second edition. Grundlehren der Mathematischen Wissenschaften [Fundamental Principles of Mathematical Sciences], 302. Springer-Verlag, Berlin, 2004. xii+635 pp. ISBN: 3-540-20488-1