Invariant Hilbert scheme resolution of Popov's SL(2)-varieties II: the non-toric case

2018/09/05 by Kubota, Ayako
#Algebraic Geometry (math.AG) #FOS: Mathematics

paper · doi:10.48550/arxiv.1809.01533

Abstract

This article is a continuation of [Kub18], which proves that if a 3-dimensional affine normal quasihomogeneous SL(2)-variety E is toric, then it has an equivariant resolution of singularities given by an invariant Hilbert scheme \mathcal H. In this article, we consider the case where E is non-toric and show that the Hilbert-Chow morphism γ: \mathcal H → E is a resolution of singularities and that \mathcal H is isomorphic to the minimal resolution of a weighted blow-up of E.

Related

• Invariant Hilbert scheme resolution of Popov's SL(2)-varieties I: the toric case
• Comments on toric varieties
• Toric Varieties in Hilbert Schemes
• The Cohomological Crepant Resolution Conjecture for the Hilbert-Chow morphisms
• Partial resolutions of Hilbert type, Dynkin diagrams, and generalized Kummer varieties