Ansatz for $(-1)^{n-1}\nabla p_n$

Soumya Dipta Banerjee; Mahir Bilen Can; Adriano Garsia

Ansatz for $(-1)^{n-1}\nabla p_n$

Algebraic Geometry 2018-08-17 v2 Combinatorics

Authors: Soumya Dipta Banerjee , Mahir Bilen Can , Adriano Garsia

Abstract

We construct a special family of equivariant coherent sheaves on the Hilbert scheme on $n$ -points in the affine plane. The equivariant Euler characteristic of these sheaves are closely related to the symmetic functions $(-1)^{n-1} \nabla p_n$ . We prove a higher cohomology vanishing result of these sheaves. It follows from the Bridgeland-King-Reid correspondence that there is an effective $S_n$ module underlying the aforementioned family of symmetric functions.

Keywords

hilbert scheme equivariant coherent sheaves symmetric functions euler characteristic higher cohomology vanishing bridgeland-king-reid correspondence

Cite

@article{arxiv.1806.05704,
  title  = {Ansatz for $(-1)^{n-1}\nabla p_n$},
  author = {Soumya Dipta Banerjee and Mahir Bilen Can and Adriano Garsia},
  journal= {arXiv preprint arXiv:1806.05704},
  year   = {2018}
}

Comments

A mistake is fixed

Ansatz for $(-1)^{n-1}\nabla p_n$

Abstract

Keywords

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