Topology of Z_3 equivariant Hilbert schemes

Autor:	Castro, Deborah, Ross, Dustin
Rok vydání:	2018
Předmět:	Mathematics - Combinatorics Mathematics - Algebraic Geometry
Druh dokumentu:	Working Paper
Popis:	Motivated by work of Gusein-Zade, Luengo, and Melle-Hern\'andez, we study a specific generating series of arm and leg statistics on partitions, which is known to compute the Poincar\'e polynomials of Z_3-equivariant Hilbert schemes of points in the plane, where Z_3 acts diagonally. This generating series has a conjectural product formula, a proof of which has remained elusive over the last ten years. We introduce a new combinatorial correspondence between partitions of n and {1,2}-compositions of n, which behaves well with respect to the statistic in question. As an application, we use this correspondence to compute the highest Betti numbers of the Z_3 equivariant Hilbert schemes. Comment: 12 pages, 11 figures; comments welcome
Databáze:	arXiv
Externí odkaz:	http://arxiv.org/abs/1810.05750 Zobrazit plný text záznamu View this record from Arxiv