Algebraic Geometry: Deformation Theory with the View of Mori Theory

2026/2027

Учебный год

ENG

Обучение ведется на английском языке

6

Кредиты

Кто читает:

Факультет математики

Статус:

Дисциплина общефакультетского пула

Когда читается:

1, 2 модуль

Преподаватель

Жгун Владимир Сергеевич

Course Syllabus

Abstract

"The aim of the course is to give the introduction to the advanced topics of algebraic geometry which are usually omitted in the standard course. The fruitfull schematic approach of Grothendieck allows to construct such objects as: Hilbert scheme (which classifies the subschemes of a given scheme), Quot scheme and scheme of morphisms of two schemes. The deformation theory studies the infinitesimal structure of these schemes, that allows to say much about the objects where the deformations are considered. This idea was used by Mori who applied the geometry of rational curves to study the birational geometry of projective varieties. In the course we shall discuss these variety of topics."