Work

Euler characteristics of affine ADE Nakajima quiver varieties via collapsing fibres

Year: 2025

Type: article

Abstract: We prove a universal substitution formula that compares generating series of Euler characteristics of Nakajima quiver varieties associated with affine ADE diagrams at generic and at certain non‐generic stability conditions via a study of collapsing fibres in the associated variation of GIT map, unifying and generalising earlier results of the last two authors with Némethi and of Nakajima. As a special case, we compute generating series of Euler characteristics of non‐commutative Quot schemes of Kleinian orbifolds. In type A and rank 1, we give a second, combinatorial proof of our substitution formula, using torus localisation and partition enumeration. This gives a combinatorial model of the fibres of the variation of GIT map, and also leads to relations between our results and the representation theory of the affine and finite Lie algebras in type A.

Source: Journal of the London Mathematical Society

DOI: 10.1112/jlms.70074

Authors: Lukas Bertsch, Ádám Gyenge, Balázs Szendrői

Institutions: University of Vienna, Budapest University of Technology and Economics

Language: English

Topic: Algebraic structures and combinatorial models

Subfield: Geometry and Topology

Field: Mathematics

Domain: Physical Sciences

Open Access status: hybrid

Estimated APC paid: $3,930

Funder: Magyar Tudományos Akadémia