The moduli space of sheaves and the generalization of MacMahon's formula

TL;DR

This paper connects a recent two-parameter generalization of MacMahon's formula to the geometry of the moduli space of sheaves on the projective plane, providing a geometric interpretation of algebraic identities.

Contribution

It offers a geometric interpretation of Vuletic's generalized MacMahon's formula through the moduli space of sheaves on the projective plane.

Findings

Ingredients of Vuletic's formula have a geometric interpretation.

The moduli space of sheaves relates to the parameters in the generalized formula.

Provides new insights into the structure of MacMahon's formula via algebraic geometry.

Abstract

Recently M. Vuletic found a two-parameter generalization of the MacMahon's formula. In this note we show that certain ingredients of her formula have a clear interpretation in terms of the geometry of the moduli space of sheaves on the projective plane.