Semi-universal family of reflexive modules over a rational double point of type \(A\). (English) Zbl 0871.14004
Maruyama, Masaki (ed.), Moduli of vector bundles. Papers of the 35th Taniguchi symposium, Sanda, Japan and a symposium held in Kyoto, Japan, 1994. New York, NY: Marcel Dekker. Lect. Notes Pure Appl. Math. 179, 65-77 (1996).
This paper is a summary of the author’s forthcoming paper “Deformation of reflexive modules over rational double points”. Let \(\text{Def}_E\) be the semi-universal deformation space of a reflexive module \(E\) over a rational double point. \(\text{Def}_E\) has a stratification whose strata correspond to some well described isomorphism classes of reflexive modules, the stratification graph being given for some examples. A versal family of a reflexive module over an \(A_n\)-singularity is given using Faltings’ construction. The author believes that the reduced part of \(\text{Def}_E\) is isomorphic with the quiver variety of a Dynkin diagram [see H. Nakajima, Duke Math. 76, No. 2, 365-416 (1994; Zbl 0826.17026)].
For the entire collection see [Zbl 0842.00034].
For the entire collection see [Zbl 0842.00034].
Reviewer: Dorin-Mihail Popescu (Bucureşti)
MSC:
| 14B07 | Deformations of singularities |
| 14D15 | Formal methods and deformations in algebraic geometry |
| 14B05 | Singularities in algebraic geometry |
| 17B67 | Kac-Moody (super)algebras; extended affine Lie algebras; toroidal Lie algebras |
