Young walls and equivariant Hilbert schemes of points in type D

TL;DR

This paper provides a combinatorial proof for the generating series of type D Young walls and refines a formula for the Euler characteristics of Hilbert schemes on type D orbifold surfaces, connecting combinatorics and algebraic geometry.

Contribution

It introduces a combinatorial proof for the multivariable generating series of type D Young walls and offers a motivic refinement for the Euler characteristic formula of Hilbert schemes.

Findings

Combinatorial proof of the generating series for type D Young walls

Motivic refinement of the Euler characteristic formula

Connection between Young walls and Hilbert schemes in type D

Abstract

We give a combinatorial proof for a multivariable formula of the generating series of type D Young walls. Based on this we give a motivic refinement of a formula for the generating series of Euler characteristics of Hilbert schemes of points on the orbifold surface of type D.