Walls for -Hilb via Reids Recipe

The three-dimensional McKay correspondence seeks to relate the geometry of crepant resolutions of Gorenstein 3-fold quotient singularities ³/ with the representation theory of the group . The first crepant resolution studied in depth was the -Hilbert scheme -HilbA3, which is also a moduli space of θ...

Ausführliche Beschreibung

Gespeichert in:
Bibliographische Detailangaben
Veröffentlicht in:Symmetry, Integrability and Geometry: Methods and Applications
Datum:2020
ISSN:1815-0659
1. Verfasser: Wormleighton, Ben
Format: Artikel
Sprache:Englisch
Veröffentlicht: Інститут математики НАН України 2020
Online Zugang:https://nasplib.isofts.kiev.ua/handle/123456789/211014
Tags: Tag hinzufügen
Keine Tags, Fügen Sie den ersten Tag hinzu!
Назва журналу:Digital Library of Periodicals of National Academy of Sciences of Ukraine
Zitieren:Walls for -Hilb via Reids Recipe. Ben Wormleighton. SIGMA 16 (2020), 106, 38 pages

Institution

Digital Library of Periodicals of National Academy of Sciences of Ukraine
Beschreibung
Zusammenfassung:The three-dimensional McKay correspondence seeks to relate the geometry of crepant resolutions of Gorenstein 3-fold quotient singularities ³/ with the representation theory of the group . The first crepant resolution studied in depth was the -Hilbert scheme -HilbA3, which is also a moduli space of θ-stable representations of the McKay quiver associated to . As the stability parameter θ varies, we obtain many other crepant resolutions. In this paper, we focus on the case where is abelian, and compute explicit inequalities for the chamber of the stability space defining -Hilb³ in terms of a marking of exceptional subvarieties of -Hilb³ called Reid's recipe. We further show which of these inequalities define walls. This procedure depends only on the combinatorics of the exceptional fibre and has applications to the birational geometry of other crepant resolutions.
ISSN:1815-0659