Кто читает:: Лаборатория алгебраической геометрии и ее приложений

Статус:: Дисциплина общефакультетского пула

Когда читается:: 1 модуль

Преподаватель

Вербицкий Михаил Сергеевич

Full 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.

Learning Objectives

Learn algebraic geometry and differential geometry in symplectic context

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 grade
Students receive a list of exercises (chosen randomly).
Final exam grade

Interim Assessment

Interim assessment (1 module)
0.7 * Final exam grade + 0.3 * Problem sheets 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

Бакалаврская программа «Математика»

Research Seminar "Hyperkähler Manifolds"