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The classical McKay correspondence
| Thesis title in Czech: | Klasická McKayova korespondence |
|---|---|
| Thesis title in English: | The classical McKay correspondence |
| Key words: | McKayova korespondence|McKayovy grafy|Dynkinovy diagramy |
| English key words: | McKay correspondence|McKay graphs|Dynkin diagrams |
| Academic year of topic announcement: | 2021/2022 |
| Thesis type: | Bachelor's thesis |
| Thesis language: | angličtina |
| Department: | Department of Algebra (32-KA) |
| Supervisor: | doc. RNDr. Jan Šťovíček, Ph.D. |
| Author: | hidden - assigned and confirmed by the Study Dept. |
| Date of registration: | 07.06.2021 |
| Date of assignment: | 07.06.2021 |
| Confirmed by Study dept. on: | 11.06.2021 |
| Date and time of defence: | 02.09.2021 09:00 |
| Date of electronic submission: | 22.07.2021 |
| Date of submission of printed version: | 22.07.2021 |
| Date of proceeded defence: | 02.09.2021 |
| Opponents: | doc. Liran Shaul, Ph.D. |
| Guidelines |
| The aim is to describe the correspondence between finite subgroups of SL(2,C) and Dynkin diagrams of types A, D and E. This includes both the algebraic correspondence in terms of McKay graphs and the geometric correspondence in terms of the minimal resolution of the corresponding singular algebraic varieties. |
| References |
| [1] I. Dolgachev, McKay correspondence, http://www.math.lsa.umich.edu/~idolga/McKaybook.pdf
[2] M. Reid, The Du Val singularities A_n, D_n, E_6, E_7, E_8, http://www.warwick.ac.uk/~masda/surf/more/DuVal.pdf [3] I. Burban, Du Val Singularities, http://www.mi.uni-koeln.de/~burban/singul.pdf [4] K. Lamotke, Regular solids and isolated singularities, Advanced Lectures in Mathematics, Friedr. Vieweg & Sohn, Braunschweig, 1986. [5] M. Žurav, Teorie invariantů pro konečné grupy, bakalářská práce na MFF UK v Praze. |
| Preliminary scope of work |
| Neformálním cílem je pochopit, jak vznikly tyto obrázky pocházející z algebraické geometrie:
https://web.northeastern.edu/martsinkovsky/p/MADL/2016/faber-slides.pdf |
| Preliminary scope of work in English |
| An informal goal is to understand how these pictures from algebraic geometry come up:
https://web.northeastern.edu/martsinkovsky/p/MADL/2016/faber-slides.pdf |