2015/12/21 by Ádám Gyenge, András Némethi, Gyenge, Ádám +3
Mathematics · #Advanced Algebra and Geometry #Algebraic Geometry (math.AG) #Algebraic Geometry and Number Theory #Algebraic structures and combinatorial models #Combinatorics (math.CO) #FOS: Mathematics #Representation Theory (math.RT)
paper · pdf · doi:10.48550/arxiv.1512.06848
openalex publication_date 2015/12/21 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
We study the geometry and topology of Hilbert schemes of points on the\norbifold surface [C2/G], respectively the singular quotient surface C2/G,\nwhere G is a finite subgroup of SL(2,C) of type A or D. We give a decomposition\nof the (equivariant) Hilbert scheme of the orbifold into affine space strata\nindexed by a certain combinatorial set, the set of Young walls. The generating\nseries of Euler characteristics of Hilbert schemes of points of the singular\nsurface of type A or D is computed in terms of an explicit formula involving a\nspecialized character of the basic representation of the corresponding affine\nLie algebra; we conjecture that the same result holds also in type E. Our\nresults are consistent with known results in type A, and are new for type D.\n