Euler characteristics of Hilbert schemes of points on simple surface singularities

DOI10.1007/s40879-018-0222-4zbMath1445.14007arXiv1512.06848OpenAlexW2962878684MaRDI QIDQ723345

Balázs Szendrői, Ádám Gyenge, András Némethi

Publication date: 31 July 2018

Published in: European Journal of Mathematics (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1512.06848

zbMATH Keywords

singularitiesEuler characteristicHilbert schemegenerating seriesYoung wall

Mathematics Subject Classification ID

Combinatorial aspects of representation theory (05E10) Enumerative problems (combinatorial problems) in algebraic geometry (14N10) Parametrization (Chow and Hilbert schemes) (14C05)

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Cites Work

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• Stable pairs and the HOMFLY polynomial
• The Hilbert scheme of a plane curve singularity and the HOMFLY polynomial of its link
• S-duality for surfaces with \(A_n\)-type singularities
• On the homology of the Hilbert scheme of points in the plane
• Quiver Grassmannians, quiver varieties and the preprojective algebra.
• Quiver varieties and Frenkel-Kac construction
• Generating functions for colored 3D Young diagrams and the Donaldson-Thomas invariants of orbifolds
• The Betti numbers of the Hilbert scheme of points on a smooth projective surface
• Basic representations of affine Lie algebras and dual resonance models
• Hilbert scheme of points on cyclic quotient singularities of type {\((p,1)\)}
• Instantons and affine algebras. I: The Hilbert scheme and vertex operators
• Kleinian singularities, derived categories and Hall algebras
• A combinatorial study on quiver varieties
• Some theorems on actions of algebraic groups
• Crystal bases of the Fock space representations and string functions
• Affine crystal graphs and two-colored partitions
• Instanton counting on blowup. I: 4-dimensional pure gauge theory
• Cranks and t-cores
• Crystal base for the basic representation of \(U_ q({\mathfrak sl}^\wedge (n))\)
• 3264 and All That
• Invariant Hilbert schemes
• On generating series of classes of equivariant Hilbert schemes of fat points
• Generalized Frobenius partitions
• Quiver Varieties, Category for Rational Cherednik Algebras, and Hecke Algebras
• CRYSTAL BASES FOR QUANTUM AFFINE ALGEBRAS AND COMBINATORICS OF YOUNG WALLS
• Quiver varieties and finite dimensional representations of quantum affine algebras
• Euler Characteristics of Hilbert Schemes of Points On Surfaces with Simple Singularities
• Symplectic reflection algebras and affine Lie algebras