2019/2020
Научно-исследовательский семинар "Гиперкэлеровы многообразия"
Статус:
Дисциплина общефакультетского пула
Где читается:
Факультет математики
Когда читается:
1 модуль
Преподаватели:
Вербицкий Михаил Сергеевич
Язык:
английский
Кредиты:
3
Контактные часы:
28
Course Syllabus
Abstract
a six weeks intense minicourse on hyperkähler and holomorphically symplectic geometry, including the detailed talks on holonomies of various manifolds, Calabi-Yau theorem, K3-surfaces, quiver spaces and, finally, if the time is left, global Torelli theorem.
Expected Learning Outcomes
- Students will learn how to apply algebraic geometry, topology and differential geometry to study of holomorphic symplectic manifolds.
Course Contents
- Levi–Civita connection and its holonomy. Berger’s classification of Riemannian holonomy.
- K3 surfaces and their deformation theory.
- Kähler manifolds and holonomy. Calabi-Yau theorem. Hyperkähler manifolds and special holonomy. Twistor spaces.
- Hyperkähler reduction and quiver spaces.
- (*) Deformations of hyperkähler manifolds. Global Torelli theorem.
Assessment Elements
- Problem sheets gradeStudents receive a list of exercises (chosen randomly).
- Final exam grade
Bibliography
Recommended Core Bibliography
- Griffiths, P., & Harris, J. (1994). Principles of Algebraic Geometry. New York: Wiley-Interscience. Retrieved from http://search.ebscohost.com/login.aspx?direct=true&site=eds-live&db=edsebk&AN=391384
Recommended Additional Bibliography
- Hartshorne, R., & American Mathematical Society. (1975). Algebraic Geometry, Arcata 1974 : [proceedings]. Providence: AMS. Retrieved from http://search.ebscohost.com/login.aspx?direct=true&site=eds-live&db=edsebk&AN=772699