2011/08/31 by Akira Ishii, Yukari Ito, Álvaro Nolla de Celis · 5 citations
Mathematics · #Advanced Algebra and Geometry #Algebraic Geometry and Number Theory #Algebraic structures and combinatorial models #Equivariant map #Hilbert scheme #Mathematics #Moduli space #Pure mathematics #math.AG #math.RT
paper · pdf · doi:10.1215/21562261-1966080
published in Kyoto journal of mathematics 53(1) (Duke University Press) · Final version. Explanations improved throughout the paper and mistakes in some statements have been corrected; (old) sections 2.2 and 3.1 have been expanded into new sections; (old) section 5 have been reorganised and several results in it have been extended. To appear in Kyoto Journal of Mathematics
arxiv created 2012/08/07 · openalex publication_date 2013/01/01 · arxiv updated 2015/01/14 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/05
In this paper we consider the iterated G-equivariant Hilbert scheme G/N-Hilb(N-Hilb) and prove that G/N-Hilb(N-Hilb(C3)) is a crepant resolution of C3/G isomorphic to the moduli space Mθ(Q) of θ-stable representations of the McKay quiver Q for certain stability condition θ. We provide several explicit examples to illustrate this construction. We also consider the problem of when G/N-Hilb(N-Hilb) is isomorphic to G-Hilb showing the fact that these spaces are most of the times different.