|SCIENTIFIC DISCIPLINARY SECTOR||MAT/03|
In the course of Geometria Superiore 1 we will introduce the theory of toric varieties, a peculiar class of algebraic varieties constructed from euclidean polytopes. This construction provides a family of special algebraic varieties whose geometric properties (such as singularities, cohomology, intersection theory, line bundles) may be described explictely by means of the geometric properties of the polytopes they are built from. Toric varieties are hence very concrete examples of algebraic varieties on which one may test general theories and conjectures. Moreover it is possible to apply on them in an explicit way many general and abstract constructions from algebraic geometry. Finally, toric varieties have several interesting applications and relations with physics, code theory, commutative algebra and much more. Thanks to these deep relations, toric varieties forms a very modern subject that is widely present in a lot of current research in algebraic geometry (and further).
The main educational outcome for the students will be to learn and work in a concrete way with many abstract tools from algebraic geometry, by applying them to the family of toric varities. This will allow students to have a clearer understanding of the general methods and notions in algebraic geometry.
The course Introduzione alla Geometria Algebrica is strongly recommended.
The course will be held in a traditional way, with lectures and exercices.
The content of the course is the following:
The suggested books and notes are the following:
VICTOR LOZOVANU (President)
The lessons will start in accordance with the academic calendar as approved by the Consiglio del Corso di Studi.
All class schedules are posted on the EasyAcademy portal.
The exam will consist in giving a talk on one of the topics that the teachers will propose.