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Faculty of Mathematics
Faculty of Mathematics
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phone/fax: +7 (495) 624-26-16
phone: +7 (495) 916-89-05

e-mail: math@hse.ru

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Alexandra Skripchenko
Sergei Lando
Scientific Supervisor – Sergei Lando
Vasily Gorbounov
Deputy Dean for Research – Vasily Gorbounov
Alexander Kolesnikov
Deputy Dean for Academic Progress – Alexander Kolesnikov
Svetlana Balaeva
Deputy Dean – Svetlana Balaeva
Vladimir Medvedev
Deputy Dean for Admissions – Vladimir Medvedev

Algebraic Geometry: Deformation Theory with the View of Mori Theory

2026/2027
Academic Year
ENG
Instruction in English
6
ECTS credits
Delivered by:
Faculty of Mathematics
Type:
Optional course (faculty)
When:
1, 2 module

Instructor

Zhgoon, Vladimir

Zhgoon, Vladimir

Course Syllabus

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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."