2023/2024
Торические многообразия
Лучший по критерию «Полезность курса для расширения кругозора и разностороннего развития»
Лучший по критерию «Новизна полученных знаний»
Статус:
Дисциплина общефакультетского пула
Кто читает:
Факультет математики
Когда читается:
3, 4 модуль
Охват аудитории:
для всех кампусов НИУ ВШЭ
Преподаватели:
Куюмжиян Каринэ Георгиевна
Язык:
английский
Кредиты:
6
Контактные часы:
72
Course Syllabus
Abstract
This is an introduction to the theory of toric varieties, which are algebraic manifolds obtained from convex polytopes by means of some wonderful explicit geometric construction. For example, the standard n-simplex gives in this way the projective space of dimension n. The advantage of the pass from polytopes to toric varieties is that the crucial combinatorial and geometric properties of polytopes predetermine the key properties of the corresponding varieties and vice versa. Almost all essential algebraic, geometric, and topological characteristics of a toric variety are explicitly computable in terms of its polytope. This makes the toric varieties very suitable for testing algebro-geometric and topological conjectures, seeking examples and counterexamples, etc.
Learning Objectives
- The seminar is intended to introduce the subject area to the students, and to offer them an opportunity to prepare and give a talk.
Expected Learning Outcomes
- Successful participants imporve their presentation skills and prepare for participation in research projects in the subject area.
Course Contents
- Affine and projective toric varieties, orbit - cone correspondence, automorphisms of affine toric varieties and locally nilpotent derivations, resolution of singularities in dimension 2 and continued fractions.
- Divisors on toric varieties.
- Cohomology groups of nonsingular toric varieties
Assessment Elements
- листкиДля сдачи листка необходимо сдать достаточное число задач из листка (6 из первого, 8 из второго, 6 из третьего, 6 из четвёртого)
- Письменный экзамен по курсу
Interim Assessment
- 2023/2024 4th module0.4 * Письменный экзамен по курсу + 0.3 * листки + 0.3 * листки
Bibliography
Recommended Core Bibliography
- Cox, D. A., Little, J. B., & Schenck, H. K. (2011). Toric Varieties. Providence, Rhode Island: AMS. Retrieved from http://search.ebscohost.com/login.aspx?direct=true&site=eds-live&db=edsebk&AN=971087
Recommended Additional Bibliography
- Fulton, W. (1993). Introduction to Toric Varieties. (AM-131), Volume 131. Princeton: Princeton University Press. Retrieved from http://search.ebscohost.com/login.aspx?direct=true&site=eds-live&db=edsebk&AN=1432979