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.